Neethu slide complete
•
0 likes•254 views
This document proves that if two chords AB and AC of a circle have their bisector of the angle BAC as a diameter, then the chords AB and AC are equal in length. It shows that triangles AMO and ANO are congruent since they share an angle and are on the diameter, meaning their bases AM and AN are also equal. Since the perpendicular from the center cuts chords in half, this means that AB and AC must be equal.
Report
Share
Report
Share
Download to read offline
Recommended
Neethu slide complete
AB and AC are two chords of a circle that meet at point A. AD is the bisector of angle BAC and intersects the circle at M and N. Since AD bisects angle BAC, the two angles formed at A are equal. Additionally, the angles formed by the radii to the chords are right angles, making triangles AMO and ANO congruent. Therefore, the midpoints M and N of the chords AB and AC respectively must lie on the same radius, implying that AB and AC are equal in length.
Triangle
The document discusses triangles and their properties. It defines a triangle as a closed figure formed by three intersecting lines with three sides, three angles, and three vertices. Two triangles are congruent if corresponding sides and angles are equal. There are five rules for triangle congruence based on sides and angles: SAS, ASA, AAS, SSS, and RHS. Inequalities in a triangle relate side lengths to opposite angles - the longer the side, the larger the opposite angle, and the third side is always smaller than the sum of the other two sides. The document was prepared by Vyom Bhardwaj, a student in 9th B with roll number 37.
ppt on Triangles Class 9
1. The document defines triangles and their properties including three sides, three angles, and three vertices.
2. It explains five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Some properties of triangles discussed are: angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
Best International School Hyderabad
1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
Triangles
1. The document discusses properties and congruence of triangles. It defines triangles as having three sides, three angles, and three vertices.
2. There are five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Additional properties discussed include: angles opposite equal sides are equal in an isosceles triangle, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
Mathematics project
Triangles can be classified based on the number of congruent sides. There are three types of triangles: scalene (no congruent sides), isosceles (at least two congruent sides), and equilateral (three congruent sides). Heron's formula provides a way to calculate the area of any triangle using the lengths of its three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (sum of sides divided by 2). The document also presents a researched formula for calculating the area of an equilateral triangle using only the length of one side.
Classification of triangle
This document provides an overview of triangles, including their basic definition, examples of triangles in everyday objects, different types of angles, and ways to classify triangles based on their angles and side lengths. It defines acute, right, and obtuse angles. It also explains how to determine if line segments are congruent based on their lengths. Finally, it classifies triangles as acute, right, obtuse, scalene, isosceles, or equilateral depending on their angle measures or relationships between side lengths.
R.TANUJ Maths Triangles for Class IX
1. The document discusses different types of triangles based on their sides and angles. It defines triangle congruence and presents several triangle congruence theorems including SAS, ASA, AAS, SSS, and RHS.
2. Properties of triangles such as corresponding angles and sides of congruent triangles being equal are explained. Inequalities in triangles and relationships between sides and angles are also covered.
3. Objectives of the lesson include defining triangle congruence, stating criteria for congruence, and properties of triangles like sum of angles and relationships between sides and angles.
Recommended
Neethu slide complete
AB and AC are two chords of a circle that meet at point A. AD is the bisector of angle BAC and intersects the circle at M and N. Since AD bisects angle BAC, the two angles formed at A are equal. Additionally, the angles formed by the radii to the chords are right angles, making triangles AMO and ANO congruent. Therefore, the midpoints M and N of the chords AB and AC respectively must lie on the same radius, implying that AB and AC are equal in length.
Triangle
The document discusses triangles and their properties. It defines a triangle as a closed figure formed by three intersecting lines with three sides, three angles, and three vertices. Two triangles are congruent if corresponding sides and angles are equal. There are five rules for triangle congruence based on sides and angles: SAS, ASA, AAS, SSS, and RHS. Inequalities in a triangle relate side lengths to opposite angles - the longer the side, the larger the opposite angle, and the third side is always smaller than the sum of the other two sides. The document was prepared by Vyom Bhardwaj, a student in 9th B with roll number 37.
ppt on Triangles Class 9
1. The document defines triangles and their properties including three sides, three angles, and three vertices.
2. It explains five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Some properties of triangles discussed are: angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
Best International School Hyderabad
1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
Triangles
1. The document discusses properties and congruence of triangles. It defines triangles as having three sides, three angles, and three vertices.
2. There are five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Additional properties discussed include: angles opposite equal sides are equal in an isosceles triangle, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
Mathematics project
Triangles can be classified based on the number of congruent sides. There are three types of triangles: scalene (no congruent sides), isosceles (at least two congruent sides), and equilateral (three congruent sides). Heron's formula provides a way to calculate the area of any triangle using the lengths of its three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (sum of sides divided by 2). The document also presents a researched formula for calculating the area of an equilateral triangle using only the length of one side.
Classification of triangle
This document provides an overview of triangles, including their basic definition, examples of triangles in everyday objects, different types of angles, and ways to classify triangles based on their angles and side lengths. It defines acute, right, and obtuse angles. It also explains how to determine if line segments are congruent based on their lengths. Finally, it classifies triangles as acute, right, obtuse, scalene, isosceles, or equilateral depending on their angle measures or relationships between side lengths.
R.TANUJ Maths Triangles for Class IX
1. The document discusses different types of triangles based on their sides and angles. It defines triangle congruence and presents several triangle congruence theorems including SAS, ASA, AAS, SSS, and RHS.
2. Properties of triangles such as corresponding angles and sides of congruent triangles being equal are explained. Inequalities in triangles and relationships between sides and angles are also covered.
3. Objectives of the lesson include defining triangle congruence, stating criteria for congruence, and properties of triangles like sum of angles and relationships between sides and angles.
right spherical triangle. trigonometry
This document discusses spherical trigonometry and spherical triangles. It defines key terms like spherical trigonometry, great circles, and spherical triangles. It also outlines Napier's rules for solving right spherical triangles and the six cases for solving oblique spherical triangles using different given parts. Examples are provided to illustrate applications of solving and finding the area of spherical triangles.
Triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles. They can also be classified based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Congruent triangles can be proven using the SSS, SAS, ASA, AAS, or RHS criteria which compare corresponding sides and angles. Important parts of a triangle include the median, altitude, angle bisector, and perpendicular bisector. The triangle inequality states that the sum of any two sides must be greater than the third side. Important points related to triangles are the incenter, circumcenter,
14 4 secant-tangent angles
Secant-tangent angles are formed when a secant line intersects a tangent line either on or outside of a circle. If the vertex is outside the circle, the degree measure is half the difference between the intercepted arcs. If the vertex is on the circle, the degree measure is half the intercepted arc. When two tangent lines form an angle, the degree measure is also half the difference between the intercepted arcs.
Triangle &types by sides
The power point explains the concept of triangles and its types.It also helps us to understand the types of triangle by its sides.
Geometry/Notes 10.6
This document discusses secants, tangents, and angle measures related to circles. It defines a secant as a line that intersects a circle at two points and presents three theorems relating the measures of angles formed by secants and tangents to the measures of the arcs they intercept. Examples demonstrate using the theorems to find measures of angles and arcs. The lesson plan is to take two days, with the first day covering notes and the second reviewing related material and giving a quiz.
Angles and sides of a triangle
The document discusses the relationships between angles and sides in triangles. The longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangles can be classified as right, acute, or obtuse based on comparing the sum of the squares of two sides to the square of the third side - right if equal, acute if greater than, and obtuse if less than. Examples are given to demonstrate classifying triangles as acute or obtuse.
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...Harish Chandra Rajpoot
All the important parameters of a spherical triangle have been derived by Mr H.C. Rajpoot by using simple geometry & trigonometry. All the articles (formula) are very practical & simple to apply in case of a spherical triangle to calculate all its important parameters such as solid angle, covered surface area, interior angles etc. & also useful for calculating all the parameters of the corresponding plane triangle obtained by joining all the vertices of a spherical triangle by straight lines. These formula can also be used to calculate all the parameters of the right pyramid obtained by joining all the vertices of a spherical triangle to the center of sphere such as normal height, angle between the consecutive lateral edges, area of base etc.Circles IX
Vaibhav Goel presented on circles and their properties. The presentation included definitions of key circle terms like radius, diameter, chord, and arc. It also proved several theorems: equal chords subtend equal angles at the center; a perpendicular from the center bisects a chord; there is one circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the angle an arc subtends at the center is double that at any other point. The presentation concluded that angles in the same segment are equal and cyclic quadrilaterals have opposite angles summing to 180 degrees.
Medians & altitudes of a triangle
The three medians of any triangle are concurrent and intersect at the triangle's centroid. The centroid is always inside the triangle and is located 2/3 of the distance from each vertex to the midpoint of the opposite side. The orthocenter, where the three altitudes intersect, is inside an acute triangle, on the right angle vertex of a right triangle, and outside an obtuse triangle.
Triginometry
The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.
4 triangles
This document defines and classifies triangles based on the lengths of their sides and the measures of their interior angles. It explains that triangles can be equilateral, isosceles, or scalene based on whether their sides are all equal, two sides are equal, or all sides are unequal. Triangles can also be right, obtuse, or acute based on whether they have a 90 degree angle, an angle over 90 degrees, or all angles under 90 degrees. The document provides examples and diagrams to illustrate different types of triangles.
Trigonometry part 1 and 2
This document discusses trigonometry and its applications. It defines trigonometry as the study of relationships between sides and angles of triangles. It introduces trigonometric ratios like sine, cosine, and tangent and defines them in terms of right triangles. It discusses trigonometric ratios of complementary angles and specific angles like 30, 45, and 60 degrees. It also covers trigonometric identities like the Pythagorean identity and cofunction identities. Finally, it discusses how trigonometry can be used to calculate heights and distances without direct measurement using concepts like line of sight, angle of elevation, and angle of depression.
Circles class 9
1) The document discusses 10 theorems related to circles. Theorem 1 proves that equal chords of a circle subtend equal angles at the centre using congruent triangles.
2) Theorem 6 proves that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle using angles on parallel lines.
3) Theorems 9 concludes that angles in the same segment of a circle are equal based on Theorem 6 and the definition of angles formed in a segment.
Lines and angles [cbse 9 maths]
This document defines and describes various types of angles and lines. It discusses collinear points, acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pairs of angles, vertically opposite angles, intersecting and non-intersecting lines, and two axioms regarding angles formed by rays on lines.
CH 10 CIRCLE PPT NCERT
1. The document defines key terms related to circles such as radius, diameter, center, chord, arc, and sector.
2. It presents 8 theorems about properties of circles and relationships between chords, arcs, angles, and points on a circle. The theorems prove properties such as equal chords subtend equal angles at the center, angles subtended by an arc are double the angle at any other point on the circle, and if a line segment subtends equal angles at two points, all four points lie on a circle.
3. Diagrams and formal proofs using triangle congruence or properties of angles are provided for each theorem.
Properties of circle
Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors
Circle geometry
This document defines circle geometry terminology like chord, arc, inscribed angle, and central angle. It then presents 5 circle theorems: 1) the perpendicular bisector of a chord passes through the circle's center, 2) congruent chords are equidistant from the center, 3) the measure of a central angle is equal to twice the measure of the angle at the circumference, 4) angles subtended by the same arc are equal, and 5) an angle subtended by a diameter is a right angle. It also states that opposite angles in a cyclic quadrilateral add to 180 degrees.
Using triangle congruence.
This document discusses triangle congruence and relationships between sides and angles of triangles. It introduces several theorems regarding isosceles, equilateral, and right triangles including: if two sides of a triangle are congruent, the angles opposite them are also congruent; if two angles of a triangle are congruent, the sides opposite them are also congruent; and if corresponding parts of two right triangles are congruent, the triangles are congruent. Examples are provided to demonstrate applying these theorems.
Area of sectors & segment ananya
This document discusses the areas of circular sectors and segments. It defines a sector as the region between two radii and an arc, and provides a formula to calculate the area of a sector based on its central angle and radius. A segment is defined as the region between a chord and arc, and the document explains that the area of a segment can be calculated by taking the area of its corresponding sector and subtracting the area of the triangular portion cut off by the chord.
Similar triangles
This document covers several theorems regarding similar triangles: AAA, AA, and SAS similarity theorems state that if corresponding angles or sides are proportional, the triangles are similar. The SSS and L-L theorems for right triangles also make claims of similarity based on proportional sides. Examples demonstrate applying these theorems to determine if triangles are similar and to find missing side lengths. The proportional segments theorem is also described as relating ratios of line segments cut by parallel lines.
Benefits of Wood Flooring
Give your home natural and unique look with Distressed floorboards which have low maintenance and cost.
20151026_Taller ITENE_Javier Mínguez
Este documento resume la situación actual y los planes futuros del IVACE, la agencia de apoyo a la innovación de la Comunidad Valenciana. Resume las convocatorias de apoyo a la I+D+i empresarial de 2014 y 2015, mostrando los proyectos solicitados y apoyados y la inversión inducida. Explica que en 2016 se consolidará el apoyo a la I+D+i empresarial, especialmente de PYMES, innovación y cooperación, con énfasis en el impacto. Se aproximará más al territorio y ofrecerá servicios de
More Related Content
What's hot
right spherical triangle. trigonometry
This document discusses spherical trigonometry and spherical triangles. It defines key terms like spherical trigonometry, great circles, and spherical triangles. It also outlines Napier's rules for solving right spherical triangles and the six cases for solving oblique spherical triangles using different given parts. Examples are provided to illustrate applications of solving and finding the area of spherical triangles.
Triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles. They can also be classified based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Congruent triangles can be proven using the SSS, SAS, ASA, AAS, or RHS criteria which compare corresponding sides and angles. Important parts of a triangle include the median, altitude, angle bisector, and perpendicular bisector. The triangle inequality states that the sum of any two sides must be greater than the third side. Important points related to triangles are the incenter, circumcenter,
14 4 secant-tangent angles
Secant-tangent angles are formed when a secant line intersects a tangent line either on or outside of a circle. If the vertex is outside the circle, the degree measure is half the difference between the intercepted arcs. If the vertex is on the circle, the degree measure is half the intercepted arc. When two tangent lines form an angle, the degree measure is also half the difference between the intercepted arcs.
Triangle &types by sides
The power point explains the concept of triangles and its types.It also helps us to understand the types of triangle by its sides.
Geometry/Notes 10.6
This document discusses secants, tangents, and angle measures related to circles. It defines a secant as a line that intersects a circle at two points and presents three theorems relating the measures of angles formed by secants and tangents to the measures of the arcs they intercept. Examples demonstrate using the theorems to find measures of angles and arcs. The lesson plan is to take two days, with the first day covering notes and the second reviewing related material and giving a quiz.
Angles and sides of a triangle
The document discusses the relationships between angles and sides in triangles. The longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangles can be classified as right, acute, or obtuse based on comparing the sum of the squares of two sides to the square of the third side - right if equal, acute if greater than, and obtuse if less than. Examples are given to demonstrate classifying triangles as acute or obtuse.
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...Harish Chandra Rajpoot
All the important parameters of a spherical triangle have been derived by Mr H.C. Rajpoot by using simple geometry & trigonometry. All the articles (formula) are very practical & simple to apply in case of a spherical triangle to calculate all its important parameters such as solid angle, covered surface area, interior angles etc. & also useful for calculating all the parameters of the corresponding plane triangle obtained by joining all the vertices of a spherical triangle by straight lines. These formula can also be used to calculate all the parameters of the right pyramid obtained by joining all the vertices of a spherical triangle to the center of sphere such as normal height, angle between the consecutive lateral edges, area of base etc.Circles IX
Vaibhav Goel presented on circles and their properties. The presentation included definitions of key circle terms like radius, diameter, chord, and arc. It also proved several theorems: equal chords subtend equal angles at the center; a perpendicular from the center bisects a chord; there is one circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the angle an arc subtends at the center is double that at any other point. The presentation concluded that angles in the same segment are equal and cyclic quadrilaterals have opposite angles summing to 180 degrees.
Medians & altitudes of a triangle
The three medians of any triangle are concurrent and intersect at the triangle's centroid. The centroid is always inside the triangle and is located 2/3 of the distance from each vertex to the midpoint of the opposite side. The orthocenter, where the three altitudes intersect, is inside an acute triangle, on the right angle vertex of a right triangle, and outside an obtuse triangle.
Triginometry
The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.
4 triangles
This document defines and classifies triangles based on the lengths of their sides and the measures of their interior angles. It explains that triangles can be equilateral, isosceles, or scalene based on whether their sides are all equal, two sides are equal, or all sides are unequal. Triangles can also be right, obtuse, or acute based on whether they have a 90 degree angle, an angle over 90 degrees, or all angles under 90 degrees. The document provides examples and diagrams to illustrate different types of triangles.
Trigonometry part 1 and 2
This document discusses trigonometry and its applications. It defines trigonometry as the study of relationships between sides and angles of triangles. It introduces trigonometric ratios like sine, cosine, and tangent and defines them in terms of right triangles. It discusses trigonometric ratios of complementary angles and specific angles like 30, 45, and 60 degrees. It also covers trigonometric identities like the Pythagorean identity and cofunction identities. Finally, it discusses how trigonometry can be used to calculate heights and distances without direct measurement using concepts like line of sight, angle of elevation, and angle of depression.
Circles class 9
1) The document discusses 10 theorems related to circles. Theorem 1 proves that equal chords of a circle subtend equal angles at the centre using congruent triangles.
2) Theorem 6 proves that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle using angles on parallel lines.
3) Theorems 9 concludes that angles in the same segment of a circle are equal based on Theorem 6 and the definition of angles formed in a segment.
Lines and angles [cbse 9 maths]
This document defines and describes various types of angles and lines. It discusses collinear points, acute angles, right angles, obtuse angles, straight angles, reflex angles, complementary angles, supplementary angles, adjacent angles, linear pairs of angles, vertically opposite angles, intersecting and non-intersecting lines, and two axioms regarding angles formed by rays on lines.
CH 10 CIRCLE PPT NCERT
1. The document defines key terms related to circles such as radius, diameter, center, chord, arc, and sector.
2. It presents 8 theorems about properties of circles and relationships between chords, arcs, angles, and points on a circle. The theorems prove properties such as equal chords subtend equal angles at the center, angles subtended by an arc are double the angle at any other point on the circle, and if a line segment subtends equal angles at two points, all four points lie on a circle.
3. Diagrams and formal proofs using triangle congruence or properties of angles are provided for each theorem.
Properties of circle
Some properties of tangents, secants and chords, Angles formed by intersecting chords, tangent and chord and two secants, Chords and their arcs, Segments of chords secants and tangents, Lengths of arcs and areas of sectors
Circle geometry
This document defines circle geometry terminology like chord, arc, inscribed angle, and central angle. It then presents 5 circle theorems: 1) the perpendicular bisector of a chord passes through the circle's center, 2) congruent chords are equidistant from the center, 3) the measure of a central angle is equal to twice the measure of the angle at the circumference, 4) angles subtended by the same arc are equal, and 5) an angle subtended by a diameter is a right angle. It also states that opposite angles in a cyclic quadrilateral add to 180 degrees.
Using triangle congruence.
This document discusses triangle congruence and relationships between sides and angles of triangles. It introduces several theorems regarding isosceles, equilateral, and right triangles including: if two sides of a triangle are congruent, the angles opposite them are also congruent; if two angles of a triangle are congruent, the sides opposite them are also congruent; and if corresponding parts of two right triangles are congruent, the triangles are congruent. Examples are provided to demonstrate applying these theorems.
Area of sectors & segment ananya
This document discusses the areas of circular sectors and segments. It defines a sector as the region between two radii and an arc, and provides a formula to calculate the area of a sector based on its central angle and radius. A segment is defined as the region between a chord and arc, and the document explains that the area of a segment can be calculated by taking the area of its corresponding sector and subtracting the area of the triangular portion cut off by the chord.
Similar triangles
This document covers several theorems regarding similar triangles: AAA, AA, and SAS similarity theorems state that if corresponding angles or sides are proportional, the triangles are similar. The SSS and L-L theorems for right triangles also make claims of similarity based on proportional sides. Examples demonstrate applying these theorems to determine if triangles are similar and to find missing side lengths. The proportional segments theorem is also described as relating ratios of line segments cut by parallel lines.
What's hot (20)
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...
Mathematical Analysis of Spherical Triangle (Spherical Trigonometry by H.C. R...
Viewers also liked
Benefits of Wood Flooring
Give your home natural and unique look with Distressed floorboards which have low maintenance and cost.
20151026_Taller ITENE_Javier Mínguez
Este documento resume la situación actual y los planes futuros del IVACE, la agencia de apoyo a la innovación de la Comunidad Valenciana. Resume las convocatorias de apoyo a la I+D+i empresarial de 2014 y 2015, mostrando los proyectos solicitados y apoyados y la inversión inducida. Explica que en 2016 se consolidará el apoyo a la I+D+i empresarial, especialmente de PYMES, innovación y cooperación, con énfasis en el impacto. Se aproximará más al territorio y ofrecerá servicios de
Presentation_NEW.PPTX
This one sentence document does not provide enough context or information to create an accurate 3 sentence summary. The document contains only one word without any other details.
Mirian
As árvores purificam o ar, ajudam na preservação ambiental e fornecem sombra e alimentos. No Dia da Árvore, devemos proteger, lutar, defender e plantar árvores para cooperar na preservação do verde, que é fonte da nossa respiração e depende do planeta.
Northeast Iceland
Jökulsárgljúfur National Park features dramatic geological formations like Ásbyrgi canyon and Dettifoss waterfall. The Krafla volcanic region includes Stóra-Viti crater and geothermal areas around Hverir with boiling mud pots and steam vents. Mývatn lake has pseudocraters, lava fields, and the steamy Grjótagjá fissure hot springs. Dimmuborgir lava formations and Hverfell tephra cone offer scenic views of this geologically diverse northern Iceland landscape.
Suðuroy, Faroe Islands
This document provides a summary of the author's trip to Suðuroy, the southernmost island in the Faroe Islands. Some of the key places visited include Tvøroyri, the largest town on Suðuroy, and Fámjin, the smallest village. In Tvøroyri, the author explores an old harbor general store that is now a museum, café, and pub. In Fámjin, the author learns about the history of the first Faroese national flag, called the Merkið flag. The trip concludes with a foggy sunset ferry ride back to Tórshavn from Suðuroy.
S012056331500025 x s300_es
Este documento presenta nuevas recomendaciones basadas en evidencia para el manejo perioperatorio de la anticoagulación oral con warfarina en pacientes con alto riesgo de tromboembolismo que serán sometidos a la implantación de dispositivos de estimulación cardíaca. Se actualizó la evidencia a través de revisiones sistemáticas y ensayos clínicos recientes, lo que llevó a una recomendación fuerte a favor de continuar la anticoagulación con warfarina durante el procedimiento en lugar de realizar terapia puente con he
Zebra gc420t
Zebra GC420T adalah printer barcode dengan teknologi thermal transfer yang menawarkan kinerja tinggi dengan harga kompetitif untuk aplikasi desktop. Printer ini memiliki desain kompak dengan prosesor 32-bit dan memori 8 MB untuk throughput label yang cepat.
Magento development outsourcing company
Are you Searching for magento development outsourcing company? Our group of professinal experts gives impeccable web advancement answers for your venture.
Como Hacer Ensalada de Taco Cuencos con Tortillas de Harina y un Bollo de Pan
La tortilla es apodado el "pan de Mexico", no obstante, se ha desarrollado de manera tan significati...
Gonder Architecture
Most of the structures in Gonder, the former capital of Ethiopia, were built in the 16th-17th centuries during the rule of Emperor Fasiladas. These included 44 churches, fortified palaces like Fasiladas' Palace and Iyasu's Castle, and other buildings constructed of alternating stone and mortar layers. Iyasu's Castle was particularly ornate, decorated with ivory, mirrors, gold and paintings. After conquering Ethiopia in 1936, Italians developed commercial and governmental districts north of the historic city.
AIR_ENERGY_Hose&Coupler_Brochure_EMAIL
This document provides information about Air Energy, a company that supplies hoses, reels, and couplers for compressed air systems. It discusses Air Energy's commitment to safety and compliance with WHS regulations. It also highlights the benefits of CEJN couplers such as their extremely low pressure drop, high flow rates, and potential cost savings compared to other brands due to reduced electricity usage. Technical specifications are provided for CEJN Series 315 and 320 couplers.
Architecture Resume
The document provides a profile for an individual seeking an entry-level position in architecture. It outlines their skills in programs like AutoCAD, Photoshop and Revit as well as skills in modeling, rendering and presentations. Their education includes a Bachelor's degree in Architecture from Philadelphia University with a photography minor. Recent work experience includes roles as an Architectural Coordinator and Technical Researcher providing assistance with project presentations, visualizations and replicating architectural drawings.
FANV y cardioversión: ¿Qué aportan los NACOs?
Fibrilación Auricular no valvular y cardioversión eléctrica: ¿qué aportan los NACO?
Jueves, 26 de Junio de 2014 19:00h
http://cvenaco.secardiologia.es
FANV y cardioversión: ¿Qué aportan los NACOs?
Dr Alfonso Macías
Unidad de Arritmias Servicio de Cardiología
HGNS Prado, Talavera de la Reina
Kit communication Téléthon2016
Vous êtes organisateur de manifestation ?
Vous trouverez l'ensemble des actions de communication prévues pour accroître la visibilité de votre manifestation.
Plano Diretor de Metas da PMBA - 2015 a 2018
O documento apresenta o Plano Diretor de Metas da Polícia Militar da Bahia para os próximos anos, com o objetivo de estabelecer ações para garantir a segurança pública no estado de forma eficiente. O plano define cinco diretrizes principais e inúmeros projetos a serem implementados, focando na reconstrução da imagem institucional, proteção à vida, fortalecimento da corregedoria, valorização dos policiais e modernização do policiamento.
Compressors and its applications
The concept of air compressor and its application is explained in detail with necessary calculations too.
Antiarritmicos
Los antiarrítmicos ejercen su acción modificando los tiempos del potencial de acción de la célula miocárdica. Se clasifican en 4 grupos según su mecanismo de acción: Grupo I (bloqueadores de canales de sodio), Grupo II (bloqueadores beta), Grupo III (bloqueadores de canales de potasio) y Grupo IV (bloqueadores de canales de calcio). Cada grupo incluye fármacos específicos, sus mecanismos de acción, indicaciones y efectos adversos.
Viewers also liked (20)
Como Hacer Ensalada de Taco Cuencos con Tortillas de Harina y un Bollo de Pan
Como Hacer Ensalada de Taco Cuencos con Tortillas de Harina y un Bollo de Pan
Similar to Neethu slide complete
Case study on circles
This document summarizes key concepts about circles. It defines circles and related terms like radius, diameter, chord, arc, and sector. It presents 8 theorems about angles subtended by chords and arcs, perpendiculars from the center to chords, circles through 3 points, equal chords and their distances from the center, and cyclic quadrilaterals. The concluding section summarizes that equal chords and arcs have corresponding relationships, angles in the same segment are equal, and properties of cyclic quadrilaterals. The document provides definitions, proofs, and conclusions about geometric properties of circles.
circles-131126094958-phpapp01.pdf
Hey to go back to m Al and resume to this email and resume y to the measure of interest in and out to go back and resume to this post to you y y y y y y y y y t y y y y y y to y y to y to the measure and resume for your help to learn to learn to learn to learn y y u yum install the world of SRP RQS PRQ PQS to go back to m Al to be a t shirt 👕 and go for the world 🌎 to be a t y to the to do the world i the world 🌎 and pink y to y y u can you must i and white 🤍 to be a I will be in and pink rod is Shreya aur Priyanshi and resume tow bar 🍺 to be a t y t y to the to go in I will be in the measure to be a t y t y to the world 🌍 to go to go with the world of interest in the morning 🌄🌄🌄🌄🌄🌄🌄🌅🌅🌅 to be a good mood to this email ✉️✉️📨 to go to go to go with you and your help in the morning 🌄 to be in and pink y to y y u yum 😋😋😋😋😋😋😋😋😋 to go to go to go to this email 📨📨📨 to go to be a good 😊😊😊 to go to go with you and pink and resume for your I I am in the measure to go to go I I I I I I I am in the measure of my friends go for it to go with you to get scholarship to this video 📸📸📸📸📸 to go to reel featuring David and resume for two 🕑🕑🕑 to go I have to check the to you y u sir to be in touch and white 🐻❄️🐻❄️ to be of any kind and white 🐻❄️🐻❄️ to go with you and your help and white 🐻❄️🐻❄️🐻❄️🐻❄️🐻❄️🐻❄️ to be in and out go back to you and pink y u can you send the measure of my to be a t to this video 📸📸📸 to go with you and pink y u sir to send the measure to be of interest in our country and white 🐻❄️🐻❄️🐻❄️🐻❄️ to go to you y y to y u yum 😋😋 to go to m go to sleep 😴😴😴😴😴 to be in touch with you must i to be of any other information to you must have been working in a little bit more time to get scholarship for two 🕑🕑🕑🕑 to be a little t to a t shirt 🎽🎽🎽🎽 to go to go to go to go to school 🏫🏫🏫 to be a little t y t to go to learn y u can be of SRP to be in the world 🌍🌍 to go to learn more about the measure to be of any action taken to be a little bit of interest for you must i to go with a t to go with the same shoes like to know about this video is currently a good 😊😊😊😊😊😊😊 to be of SRP to be in and out go talking with a t shirt 🎽🎽🎽 to go to go to go with a good 😊😊😊 to go to go to go to go with you must i to go with the measure of interest in the morning 🌅🌅 to go with a little more than a t y y y y y y y y y y y y y u sir to be of any action in and out go to sleep now and white striped shirt and they are in a t y y to go to go with the same to u dear and white striped shirt and pink y to go with a good 😊😊😊😊😊 to go to go to go to go to go to go to go to go to go to go to go to go to go to go to go to go to go to go with the same to you must have been a little yyyyyyy to go to go to go to go to go to go to go to go to go to go to go to go to go to go to sleep 💤😴😴😴 and resume for your help to learn to learn by you and your family a very happy birthday dear fr
CHAPTER -10 CIRCLE 9TH CLASS NCERT
The document defines key terms related to circles such as radius, diameter, chord, arc, and sector. It discusses properties of circles including: angles subtended by chords; perpendiculars from the center to chords bisect chords; there is one unique circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the sums of opposite angles in a cyclic quadrilateral are 180 degrees. The document concludes by summarizing key properties of circles.
Maths Circle PPT Class10
This document summarizes key terms and theorems related to circles:
1. It defines circles and related terms like radius, diameter, chord, arc, and sector.
2. It describes theorems like equal chords subtend equal angles at the center, and conversely if angles are equal then chords are equal.
3. Other concepts covered include perpendiculars from the center bisect chords, congruent arcs subtend equal angles, and cyclic quadrilaterals have opposite angles summing to 180 degrees.
PPT ON TRIANGLES FOR CLASS X
1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
Geometry theorem triangles and Circles
Here are some important formulas on Congruent Triangles, Exterior Angles, Equal sides, Circle (Arc Theorem), Tangent.
Circle geometry
1) Laws of circle geometry include angles subtended on the same arc being equal, angles formed by a diameter and circumference forming a right angle, and tangents forming right angles with radii.
2) Proofs for these laws involve splitting triangles formed using radii and points on the circumference into isosceles triangles, and using properties of angles in triangles and circles.
3) Additional circle geometry concepts covered are tangents only touching circles at one point, alternate segment theorem stating corresponding angles are equal, and cyclic quadrilaterals having opposite angles summing to 180 degrees.
power point presentation..slides
This document defines key terms related to circles such as radius, diameter, and chords. It states that the length of all chords at equal distances from the center of a circle are equal. This is proven using properties of right triangles and perpendicular bisectors - by showing two chords form two congruent right triangles with the radius, their lengths must be equal.
CIRCLES
This document discusses various theorems related to circles:
1. Equal chords of a circle subtend equal angles at the centre.
2. If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
3. The perpendicular from the centre of a circle to a chord bisects the chord.
Maths sa 2 synopsis
The document provides information about topics in grade 9 math, including:
1) Linear equations in two variables and their graphical representations as lines.
2) Properties of quadrilaterals such as parallelograms, and how to classify them.
3) Finding areas of parallelograms, triangles, and how these shapes are related.
4) Properties of circles such as angles subtended by chords and arcs.
Circles
1. The document defines various terms related to circles like arc, chord, diameter, radius, and discusses 13 theorems related to circles.
2. The theorems discuss properties of circles like equal chords subtend equal angles, a perpendicular from the center bisects a chord, and the angle subtended by an arc at the center is double the angle at any other point on the circle.
3. The document concludes with a 16 point summary of the key topics covered related to defining circles and their geometric properties.
Geometry - Mathematics - 9th Grade by Slidesgo.pptx
The document is a student's report on circles and geometry that includes definitions of key circle terms like radius, diameter, chord, and arc. It also proves several circle theorems, such as equal chords subtending equal angles at the center and the perpendicular from the center bisecting a chord. Additionally, it discusses drawing a circle through three points and the relationship between arcs and their corresponding chords. The report aims to explain fundamental circle concepts and their properties.
Maths ppt of class 9 CBSE topic Triangles
1. Two triangles are congruent if their corresponding sides and angles are equal. This can be determined through various criteria like SAS, ASA, AAS, SSS, or RHS.
2. A triangle has several properties - angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
3. The document discusses the definitions, criteria, and properties of triangles, including what makes two triangles congruent.
Triangles
The document discusses different types of triangles and the properties used to determine if two triangles are congruent. It defines triangles and their components like sides and angles. It then explains the different types of triangles based on side lengths and angle measures. The properties used to prove triangle congruence are side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and hypotenuse-side (RHS).
mathsproject-
1. The document discusses properties and congruence criteria of triangles. It defines triangles as having three sides, three angles, and three vertices.
2. There are five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Additional properties discussed include: angles opposite equal sides are equal; sides opposite equal angles are equal; the sum of any two sides is greater than the third side.
triangles ppt.pptx
1. The document discusses properties and congruence criteria of triangles. It defines triangles as having three sides, three angles, and three vertices.
2. There are five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Additional properties discussed include: angles opposite equal sides are equal; sides opposite equal angles are equal; the sum of any two sides is greater than the third side.
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEd
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEd
A compilation of Math III learning modules for EASE which can be alternate for Grade 9 Mathematics.
Free!
Circle.pptx
This document contains multiple geometry problems involving circles, chords, radii, and angles. The problems can be summarized as follows:
1) Several problems involve calculating distances from circle centers to chords of given lengths or radii of circles given distances between chords and centers.
2) Other problems involve finding lengths of chords or distances between parallel chords given properties like one chord's length, the distance between chords, or a circle's diameter.
3) Some problems prove properties of angles or segments related to chords, such as angles subtended by arcs or segments drawn from circle centers to chords.
Congruents of Triangle
Triangles are congruent if they have the same three sides and three angles. Congruence can be proven using various criteria: SAS (side-angle-side), ASA (angle-side-angle), SSS (side-side-side), RHS (right angle-hypotenuse-side). Properties of triangles include: angles opposite equal sides of an isosceles triangle are equal; sides opposite equal angles are equal; the angle opposite the longer side is larger; the side opposite the longer angle is longer; the sum of any two sides is greater than the third side.
Congruent of Triangles
Triangles are congruent if they have the same three sides and three angles. Congruence can be proven using various criteria: SAS (side-angle-side), ASA (angle-side-angle), SSS (side-side-side), RHS (right angle-hypotenuse-side). Properties of triangles include: angles opposite equal sides of an isosceles triangle are equal; sides opposite equal angles are equal; the angle opposite the longer side is larger; the side opposite the longer angle is longer; the sum of any two sides is greater than the third side.
Similar to Neethu slide complete (20)
Geometry - Mathematics - 9th Grade by Slidesgo.pptx
Geometry - Mathematics - 9th Grade by Slidesgo.pptx
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEd
Grade 9 (Alternate) Mathematics III - Learning Modules for EASE Program of DepEd
Recently uploaded
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
Walmart Business+ and Spark Good for Nonprofits.pdf
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdMain Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Recently uploaded (20)
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Neethu slide complete
- 1. WELCOME
- 2. CIRCLE
- 3. A circle can be displaced as the locus of a point which moves at a specifics distance from a specific distance from a specific point
- 4. AB and ac are two chords of a circle and the bisector of ˂BAC is a diameter of the circle. Prove that AB=AC
- 5. B C DA N M O AB and AC are the equal chords. This chords join with point A. AD is the bisector of ˂ BAC . O be the center of circle. Therefore, ˂AMO = ˂ ANO = 90˚ ˂MAO = ˂NAO ( Since AD is the bisector of ˂ BAC )
- 6. Therefore, ˂AOM = ˂ AON. Why. (If two angles of two triangles are equal , then the third angle also will be equal then the third angle also will be equal.)
- 7. Therefore AMO and ANO are congruent (one side and two angles on that side of a triangle are equal to one side and two angles on that side of other triangle)
- 8. AM=AN (Corresponding sides of congruent triangles) Since the perpendicular at from the centre of the circle to the chord passes through the midpoint of the chord. Therefore M is the midpoint of AB and N is the midpoint of AC
- 9. Since AM=AN ½ AB =½AC i.e., AB =AC
- 10. THANKYOU