Area
•Download as PPTX, PDF•
1 like•292 views
This document discusses how to find the areas of various figures like triangles and rectangles. It provides the formulas for calculating the area of a triangle based on its base and height. It also states the theorem that triangles with the same base and between the same parallels have equal areas. As an application, it asks the reader to draw triangles of equal area to given triangles in different configurations using the area-preserving property of triangles between parallels. It provides some practice problems and ends by thanking the reader.
Report
Share
Report
Share
Recommended
PowerPoint Presentation
The document is a PowerPoint presentation submitted by Shiny Varghese for a mathematics class. It contains two problems - the first asks to draw triangle ABC with sides of 4cm, 5cm, and 6cm, and then draw another triangle of the same area with one side being 4cm. The second problem asks to draw triangle ABC and then draw a different triangle of the same area with sides of 6cm and 7cm.
TWO TRIANGLES HAVING THE SAME BASE AND EQUAL AREAS LIE BETWEEN THE SAME PARAL...
The document provides two examples of geometric proofs involving areas of shapes. The first example proves that a triangle's median divides it into two equal areas. It does so by drawing an altitude and showing the two resulting triangles have the same base and altitude. The second example proves the area of a quadrilateral ABCD equals the area of triangle ADE by showing two triangles on the same base and between parallel lines have equal areas.
Tugas pertemuan 7
This document contains 6 math problems involving similar triangles, similar figures, and proportional relationships: 1) Calculate lengths and determine similarity between two triangles, 2) Find values for x given similar cones, 3) Identify similar triangles in a trapezium and find values of x and y, 4) Find values of x and y given two similar triangles, 5) Name corresponding sides and find values of x and y for two similar figures, 6) Find values of x and y.
areas_of_parallelograms_and_triangles
The document discusses areas of parallelograms and triangles. It contains examples of figures that lie on the same base and between the same parallels. It also contains problems calculating the areas of various shapes formed from parallelograms and triangles. One problem involves a farmer dividing a parallelogram-shaped field into three triangular parts by drawing a line between two vertices, and requiring the crops to be sown in equal areas.
Law Of Sines; Powerpoint
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.
Quadrilateral
This document defines and describes properties of various quadrilaterals:
- Rectangles have four right angles and opposite sides of equal length. The area formula is length x width.
- Parallelograms have two pairs of parallel sides. The opposite angles are equal and adjacent angles sum to 180 degrees. Diagonals bisect each other.
- Trapezoids have one pair of parallel sides. Isosceles trapezoids have two pairs of equal angles and equal or equal length diagonals. Right trapezoids contain one right angle. The area of any trapezoid is half the product of the height and sum of the parallel sides.
Law of Cosines
The Law of Cosines is an equation that can be used to find the length of any side of a triangle if two sides and the angle between them are known. It is more versatile than the Pythagorean theorem, which only applies to right triangles. The Law of Cosines states: c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C. Several examples are provided to demonstrate using the Law of Cosines to calculate lengths and angles of triangles. Variations of the equation allow solving for a, b, or the angles instead of c.
Area of triangles and IIgm
The document discusses triangles, parallelograms, and congruent figures in geometry. It defines triangles and parallelograms, explains how to calculate their areas, and presents three theorems: 1) Parallelograms on the same base and between the same parallels have equal areas. 2) A diagonal of a parallelogram divides it into two triangles of equal area. 3) The area of a triangle in a parallelogram is equal to half the area of the parallelogram. Proofs of the theorems are provided based on properties of parallel lines, congruent triangles, and calculations of area.
Recommended
PowerPoint Presentation
The document is a PowerPoint presentation submitted by Shiny Varghese for a mathematics class. It contains two problems - the first asks to draw triangle ABC with sides of 4cm, 5cm, and 6cm, and then draw another triangle of the same area with one side being 4cm. The second problem asks to draw triangle ABC and then draw a different triangle of the same area with sides of 6cm and 7cm.
TWO TRIANGLES HAVING THE SAME BASE AND EQUAL AREAS LIE BETWEEN THE SAME PARAL...
The document provides two examples of geometric proofs involving areas of shapes. The first example proves that a triangle's median divides it into two equal areas. It does so by drawing an altitude and showing the two resulting triangles have the same base and altitude. The second example proves the area of a quadrilateral ABCD equals the area of triangle ADE by showing two triangles on the same base and between parallel lines have equal areas.
Tugas pertemuan 7
This document contains 6 math problems involving similar triangles, similar figures, and proportional relationships: 1) Calculate lengths and determine similarity between two triangles, 2) Find values for x given similar cones, 3) Identify similar triangles in a trapezium and find values of x and y, 4) Find values of x and y given two similar triangles, 5) Name corresponding sides and find values of x and y for two similar figures, 6) Find values of x and y.
areas_of_parallelograms_and_triangles
The document discusses areas of parallelograms and triangles. It contains examples of figures that lie on the same base and between the same parallels. It also contains problems calculating the areas of various shapes formed from parallelograms and triangles. One problem involves a farmer dividing a parallelogram-shaped field into three triangular parts by drawing a line between two vertices, and requiring the crops to be sown in equal areas.
Law Of Sines; Powerpoint
The document discusses the Law of Sines, which can be used to solve triangles that are not right triangles. It provides three formulas for finding the area of a triangle using two angles and one included side: Area = 1/2 * b * c * sin(A), 1/2 * a * c * sin(B), 1/2 * a * b * sin(C). It also gives the formula for the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). An example problem finds the area of a triangle given two side lengths and one angle measure.
Quadrilateral
This document defines and describes properties of various quadrilaterals:
- Rectangles have four right angles and opposite sides of equal length. The area formula is length x width.
- Parallelograms have two pairs of parallel sides. The opposite angles are equal and adjacent angles sum to 180 degrees. Diagonals bisect each other.
- Trapezoids have one pair of parallel sides. Isosceles trapezoids have two pairs of equal angles and equal or equal length diagonals. Right trapezoids contain one right angle. The area of any trapezoid is half the product of the height and sum of the parallel sides.
Law of Cosines
The Law of Cosines is an equation that can be used to find the length of any side of a triangle if two sides and the angle between them are known. It is more versatile than the Pythagorean theorem, which only applies to right triangles. The Law of Cosines states: c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C. Several examples are provided to demonstrate using the Law of Cosines to calculate lengths and angles of triangles. Variations of the equation allow solving for a, b, or the angles instead of c.
Area of triangles and IIgm
The document discusses triangles, parallelograms, and congruent figures in geometry. It defines triangles and parallelograms, explains how to calculate their areas, and presents three theorems: 1) Parallelograms on the same base and between the same parallels have equal areas. 2) A diagonal of a parallelogram divides it into two triangles of equal area. 3) The area of a triangle in a parallelogram is equal to half the area of the parallelogram. Proofs of the theorems are provided based on properties of parallel lines, congruent triangles, and calculations of area.
areas of triangles and parallelograms
The document discusses geometry and formulas for calculating the areas of different shapes. It begins by explaining how geometry originated from measuring land areas. It then reviews key concepts like planar regions and formulas for finding the areas of rectangles, squares, parallelograms, and triangles. The main part proves theorems about the areas of figures on the same base and between the same parallels, including that parallelograms in this position have equal areas, and triangles in this position have half the area of the corresponding parallelogram. It concludes by listing five proofs as examples.
Law of sine and cosines
This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.
Welcome1
The area of a triangle within a rectangle is half the area of the rectangle if they share the same base. If the triangle is required to be isosceles, the point defining the triangle's third vertex must be at the midpoint of the rectangle's other side. If the triangle must also be a right triangle, the third vertex point must be at the corner of the rectangle opposite the shared base.
Area ratio
The document discusses calculating the ratio of the areas of two triangles. It first draws a perpendicular from the point A to the base BC of the triangles. It then states that the area of triangle ABD is 1/2 times the height h times the length BD, and the area of triangle ACD is 1/2 times the height h times the length CD. Finally, it concludes that the ratio of the two areas is equal to the ratio of the lengths BD and CD.
Mathsproject 140209091923-phpapp01
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. Triangles can be classified as congruent if corresponding angles and sides are equal. There are several ways triangles can be proven congruent, including Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), Side-Side-Side (SSS), and Right-Angle-Hypotenuse (RHS). Properties of triangles discussed include isosceles triangles having two equal sides and equal angles opposite, and the theorem that the angle opposite the longer side of a triangle is larger.
8.2 Law of Cosines
The document discusses the Law of Cosines and Heron's formula for finding the area of a triangle. It provides an example of using the Law of Cosines to solve for a missing side of a triangle given two sides and the angle between them. It then uses the solved side lengths to find the other two angles of the triangle. Finally, it provides an example of using Heron's formula to calculate the area of a triangle when all three side lengths are known.
Area And Perimeter
The document defines and provides examples of calculating area and perimeter. It explains that area is measured in square units and refers to the surface space of a flat object, while perimeter is the distance around the outside edge and is measured in linear units. Examples are given of counting squares to find the area of different shapes and counting sides to determine the perimeter. Two neighbor's pools are used as examples, with Family A's pool having a larger area but Family B's pool having a greater perimeter and more side panels to clean.
Area of parallelograms and triangles
This document discusses properties of parallelograms, triangles, and calculating their areas. It defines a parallelogram as a quadrilateral with both pairs of opposite sides parallel. Properties include opposite sides being parallel and congruent. It defines a triangle as a three-sided polygon. It explains that the area of a shape is a number associated with the enclosed plane region, with equal areas for congruent shapes and the sum of areas for shapes that combine. It discusses congruent figures having equal areas but not vice versa, and that parallelograms and triangles on the same base or between parallels have equal areas.
Tugas pertemuan 5
1. The document describes how to show that two triangles are congruent by cutting out one triangle and placing it on top of the other so that their corresponding sides and angles coincide. It states that for two triangles to be congruent, their corresponding sides must have equal lengths and corresponding angles must have equal measures.
2. It then gives another example of two triangles where the sides correspond to each other (are equal in length) and states that this is sufficient to show the triangles are congruent.
3. Finally, it instructs students to look at two additional pairs of triangles and identify their corresponding sides of equal length and corresponding angles of equal measure to determine if they are congruent.
Triangle
This document provides information about different types of triangles categorized by side lengths, angle measures, and combinations of sides and angles. It defines equilateral, isosceles, scalene, acute, right, and obtuse triangles. It also discusses calculating the perimeter and area of triangles. The key points are:
- Triangles can be categorized based on equal or unequal side lengths or by angle measures.
- The sum of the interior angles of any triangle is always 180 degrees.
- The perimeter of a triangle is the sum of the lengths of its three sides.
- The area of a triangle can be calculated by multiplying one-half the base by the height.
Math12 lesson9
The document derives the Law of Sines and Law of Cosines, which relate the angles and sides of triangles. It discusses using these laws to solve oblique triangles given certain information like two angles and a side, two sides and the angle opposite one of the sides, two sides and the angle between them, or all three sides. It also covers finding the area of a triangle given two sides and the included angle, or using Heron's Formula with all three sides. Application problems demonstrate using these concepts to solve real-world geometry problems.
Geom 6point3 97
This document discusses several theorems for proving that a quadrilateral is a parallelogram:
1) If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
2) If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.
3) If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram.
The document also provides proofs of these theorems and discusses using coordinate geometry to prove sides are congruent or parallel.
Chapter 1.2
- Hales, a Greek mathematician, was the first to measure the height of a pyramid using similar triangles. He showed that the ratio of the height of the pyramid to the height of the worker was the same as the ratio of the heights of their respective shadows.
- The document discusses using similar triangles to solve problems involving finding unknown lengths, such as measuring the height of a pyramid based on the shadow lengths of the pyramid and a worker of known height.
- Examples are provided of determining if two triangles are similar based on proportional sides or equal corresponding angles, and using similarities between triangles to find unknown lengths.
Prism
This document provides information about calculating the surface area of a rectangular prism. It defines a rectangular prism as a solid figure with two pairs of parallel opposite faces that are all rectangles. It explains that the surface area is the sum of the lateral surface area and twice the base area. The lateral surface area is calculated as 2lh+2bh. The base area is 2bh. Putting it together, the total surface area is 2(lb+bh+lh).
Gch04 l5
This document discusses different methods for proving triangles congruent:
- ASA (Angle-Side-Angle) congruence can be used if two angles and the included side are congruent.
- AAS (Angle-Angle-Side) congruence can be used if two angles of one triangle are congruent to two angles of another triangle and one side included between the angles is congruent.
- HL (Hypotenuse-Leg) congruence can be used if two right triangles have one leg and the hypotenuse congruent.
Examples are provided to demonstrate applications of each method of triangle congruence.
Ppt 1
This document discusses two methods for finding the area of a quadrilateral. The first method is to divide the quadrilateral into two triangles and find the sum of their areas. The second method involves drawing a diagonal and a parallel line to form a triangle with the same area as the original quadrilateral, so only the area of the triangle needs to be calculated. In conclusion, drawing a triangle of equal area inside a quadrilateral allows the area to be found by calculating just the triangle's area.
Class 9 Cbse Maths Sample Paper Model 3
This document is a sample test paper for Class 9 mathematics. It consists of 37 total questions divided into 4 sections - Section A has 10 single mark questions, Section B has 9 two mark questions, Section C has 10 three mark questions, and Section D has 8 four mark questions. The test covers a range of mathematics topics and concepts, including geometry, algebra, trigonometry, and statistics. Students are instructed to answer all questions within the allotted time of 3 hours.
Quadrilateral
The document defines and describes different types of quadrilaterals. It states that a quadrilateral is a closed figure bounded by four line segments. The sum of the interior angles of any quadrilateral is always 360 degrees. The main types of quadrilaterals discussed are trapezium, parallelogram, rectangle, rhombus, square, and kite. Each shape is defined by the properties of the lengths and orientations of its sides.
10.4 notes
A quadrilateral is a closed shape with four line segments that intersect only at their endpoints. The sum of the interior angles of any quadrilateral is always 360 degrees. This document provides information about different types of quadrilaterals based on their properties, including whether they have parallel sides and equal angles or sides. It also includes formulas for finding the area and perimeter of rectangles.
Introduccion al marketing ESPOCH Finanzas
Este documento analiza la estrategia del océano azul de Victoria's Secret y los principios que sigue esta empresa. También incluye un análisis del chocolate Milky Way y de su empresa propietaria Mars.
Business presentation
This document summarizes a business called Tyre Fires that creates handmade fire pits from recycled wheel rims. The business is run by seven students who have experience in business competitions. Tyre Fires aims to create sustainable, high-quality fire pits customized for customers' needs. They offer various fire pit models starting at £19.99 and have negotiated deals on materials. Market research found most potential customers interested in the product.
More Related Content
What's hot
areas of triangles and parallelograms
The document discusses geometry and formulas for calculating the areas of different shapes. It begins by explaining how geometry originated from measuring land areas. It then reviews key concepts like planar regions and formulas for finding the areas of rectangles, squares, parallelograms, and triangles. The main part proves theorems about the areas of figures on the same base and between the same parallels, including that parallelograms in this position have equal areas, and triangles in this position have half the area of the corresponding parallelogram. It concludes by listing five proofs as examples.
Law of sine and cosines
This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.
Welcome1
The area of a triangle within a rectangle is half the area of the rectangle if they share the same base. If the triangle is required to be isosceles, the point defining the triangle's third vertex must be at the midpoint of the rectangle's other side. If the triangle must also be a right triangle, the third vertex point must be at the corner of the rectangle opposite the shared base.
Area ratio
The document discusses calculating the ratio of the areas of two triangles. It first draws a perpendicular from the point A to the base BC of the triangles. It then states that the area of triangle ABD is 1/2 times the height h times the length BD, and the area of triangle ACD is 1/2 times the height h times the length CD. Finally, it concludes that the ratio of the two areas is equal to the ratio of the lengths BD and CD.
Mathsproject 140209091923-phpapp01
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. Triangles can be classified as congruent if corresponding angles and sides are equal. There are several ways triangles can be proven congruent, including Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), Side-Side-Side (SSS), and Right-Angle-Hypotenuse (RHS). Properties of triangles discussed include isosceles triangles having two equal sides and equal angles opposite, and the theorem that the angle opposite the longer side of a triangle is larger.
8.2 Law of Cosines
The document discusses the Law of Cosines and Heron's formula for finding the area of a triangle. It provides an example of using the Law of Cosines to solve for a missing side of a triangle given two sides and the angle between them. It then uses the solved side lengths to find the other two angles of the triangle. Finally, it provides an example of using Heron's formula to calculate the area of a triangle when all three side lengths are known.
Area And Perimeter
The document defines and provides examples of calculating area and perimeter. It explains that area is measured in square units and refers to the surface space of a flat object, while perimeter is the distance around the outside edge and is measured in linear units. Examples are given of counting squares to find the area of different shapes and counting sides to determine the perimeter. Two neighbor's pools are used as examples, with Family A's pool having a larger area but Family B's pool having a greater perimeter and more side panels to clean.
Area of parallelograms and triangles
This document discusses properties of parallelograms, triangles, and calculating their areas. It defines a parallelogram as a quadrilateral with both pairs of opposite sides parallel. Properties include opposite sides being parallel and congruent. It defines a triangle as a three-sided polygon. It explains that the area of a shape is a number associated with the enclosed plane region, with equal areas for congruent shapes and the sum of areas for shapes that combine. It discusses congruent figures having equal areas but not vice versa, and that parallelograms and triangles on the same base or between parallels have equal areas.
Tugas pertemuan 5
1. The document describes how to show that two triangles are congruent by cutting out one triangle and placing it on top of the other so that their corresponding sides and angles coincide. It states that for two triangles to be congruent, their corresponding sides must have equal lengths and corresponding angles must have equal measures.
2. It then gives another example of two triangles where the sides correspond to each other (are equal in length) and states that this is sufficient to show the triangles are congruent.
3. Finally, it instructs students to look at two additional pairs of triangles and identify their corresponding sides of equal length and corresponding angles of equal measure to determine if they are congruent.
Triangle
This document provides information about different types of triangles categorized by side lengths, angle measures, and combinations of sides and angles. It defines equilateral, isosceles, scalene, acute, right, and obtuse triangles. It also discusses calculating the perimeter and area of triangles. The key points are:
- Triangles can be categorized based on equal or unequal side lengths or by angle measures.
- The sum of the interior angles of any triangle is always 180 degrees.
- The perimeter of a triangle is the sum of the lengths of its three sides.
- The area of a triangle can be calculated by multiplying one-half the base by the height.
Math12 lesson9
The document derives the Law of Sines and Law of Cosines, which relate the angles and sides of triangles. It discusses using these laws to solve oblique triangles given certain information like two angles and a side, two sides and the angle opposite one of the sides, two sides and the angle between them, or all three sides. It also covers finding the area of a triangle given two sides and the included angle, or using Heron's Formula with all three sides. Application problems demonstrate using these concepts to solve real-world geometry problems.
Geom 6point3 97
This document discusses several theorems for proving that a quadrilateral is a parallelogram:
1) If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
2) If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.
3) If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram.
The document also provides proofs of these theorems and discusses using coordinate geometry to prove sides are congruent or parallel.
Chapter 1.2
- Hales, a Greek mathematician, was the first to measure the height of a pyramid using similar triangles. He showed that the ratio of the height of the pyramid to the height of the worker was the same as the ratio of the heights of their respective shadows.
- The document discusses using similar triangles to solve problems involving finding unknown lengths, such as measuring the height of a pyramid based on the shadow lengths of the pyramid and a worker of known height.
- Examples are provided of determining if two triangles are similar based on proportional sides or equal corresponding angles, and using similarities between triangles to find unknown lengths.
Prism
This document provides information about calculating the surface area of a rectangular prism. It defines a rectangular prism as a solid figure with two pairs of parallel opposite faces that are all rectangles. It explains that the surface area is the sum of the lateral surface area and twice the base area. The lateral surface area is calculated as 2lh+2bh. The base area is 2bh. Putting it together, the total surface area is 2(lb+bh+lh).
Gch04 l5
This document discusses different methods for proving triangles congruent:
- ASA (Angle-Side-Angle) congruence can be used if two angles and the included side are congruent.
- AAS (Angle-Angle-Side) congruence can be used if two angles of one triangle are congruent to two angles of another triangle and one side included between the angles is congruent.
- HL (Hypotenuse-Leg) congruence can be used if two right triangles have one leg and the hypotenuse congruent.
Examples are provided to demonstrate applications of each method of triangle congruence.
Ppt 1
This document discusses two methods for finding the area of a quadrilateral. The first method is to divide the quadrilateral into two triangles and find the sum of their areas. The second method involves drawing a diagonal and a parallel line to form a triangle with the same area as the original quadrilateral, so only the area of the triangle needs to be calculated. In conclusion, drawing a triangle of equal area inside a quadrilateral allows the area to be found by calculating just the triangle's area.
Class 9 Cbse Maths Sample Paper Model 3
This document is a sample test paper for Class 9 mathematics. It consists of 37 total questions divided into 4 sections - Section A has 10 single mark questions, Section B has 9 two mark questions, Section C has 10 three mark questions, and Section D has 8 four mark questions. The test covers a range of mathematics topics and concepts, including geometry, algebra, trigonometry, and statistics. Students are instructed to answer all questions within the allotted time of 3 hours.
Quadrilateral
The document defines and describes different types of quadrilaterals. It states that a quadrilateral is a closed figure bounded by four line segments. The sum of the interior angles of any quadrilateral is always 360 degrees. The main types of quadrilaterals discussed are trapezium, parallelogram, rectangle, rhombus, square, and kite. Each shape is defined by the properties of the lengths and orientations of its sides.
10.4 notes
A quadrilateral is a closed shape with four line segments that intersect only at their endpoints. The sum of the interior angles of any quadrilateral is always 360 degrees. This document provides information about different types of quadrilaterals based on their properties, including whether they have parallel sides and equal angles or sides. It also includes formulas for finding the area and perimeter of rectangles.
What's hot (20)
Viewers also liked
Introduccion al marketing ESPOCH Finanzas
Este documento analiza la estrategia del océano azul de Victoria's Secret y los principios que sigue esta empresa. También incluye un análisis del chocolate Milky Way y de su empresa propietaria Mars.
Business presentation
This document summarizes a business called Tyre Fires that creates handmade fire pits from recycled wheel rims. The business is run by seven students who have experience in business competitions. Tyre Fires aims to create sustainable, high-quality fire pits customized for customers' needs. They offer various fire pit models starting at £19.99 and have negotiated deals on materials. Market research found most potential customers interested in the product.
Teaching expertise & scholarly presentations
The document summarizes the author's expertise in teaching and scholarly presentations. It outlines their passion for teaching across multiple courses at both the undergraduate and graduate levels. Their goal is to promote knowledge acquisition, critical thinking, and application of learning to clinical practice. They employ active learning strategies like discussions, presentations, and flipped classrooms. Student evaluations praise their engagement, knowledge, and passion for teaching. The author has also mentored 17 students and received teaching awards. They have developed new courses and curriculum.
hep27679
Caffeine treatment decreased portal pressure and ameliorated hyperdynamic circulation in cirrhotic rats through its antagonistic effects on adenosine receptors. Caffeine reduced mesenteric angiogenesis, portosystemic shunting, and hepatic angiogenesis in cirrhotic rats. These beneficial effects of caffeine were reversed by selective agonists of the adenosine A1 and A2A receptors. Caffeine may be a potential therapy for portal hypertension and its complications in cirrhosis.
Aviation as a Passion
Do you like Aviation and Airplanes then you Must see these slides .these slides contains information about aviation and airplanes.
Gous Resume
Mohammed Gous is seeking a position that allows him to use his technical, analytical, and enterprising skills. He has over 5 years of experience in desktop support, hardware and software troubleshooting, network administration, and customer support. His educational background includes a diploma in computer hardware and networking. He is proficient in desktop and network support skills such as OS installation, hardware maintenance, cabling, and remote assistance.
2-1. Startup Ecosystem in France and French Tech intro_021517
Startup Ecosystem in France and French Tech was introduced by Jonathan Lauer-Stumm, French Tech Coordinator of Expertise France in Korea.
Študentské pôžičky - 123 Pôžičky
Ste študent alebo vysokoškolák a hľadáte možnosti kde si požičať? Sú tu pre Vás študentské pôžičky a úvery, ktoré získate od štátu ale aj v banke. Viac sa dozviete v našej prezentácii.
Mtv correto
O documento descreve o programa MTV Hits, que transmite os melhores clipes musicais e interage com a audiência através das redes sociais. O programa atinge principalmente mulheres entre 18 e 24 anos e tem tido grande sucesso no Twitter, frequentemente ficando entre os assuntos mais comentados.
1-2. The UK Startup Ecosystem_021517
The UK startup ecosystem was introduced by Yejin Yoo, Investment Officer, Department of International Trade of British Embassy
Viewers also liked (11)
2-1. Startup Ecosystem in France and French Tech intro_021517
2-1. Startup Ecosystem in France and French Tech intro_021517
Similar to Area
Math 8 – triangle congruence, postulates,
The document provides information about triangle congruence, including:
1. There are three postulates for proving triangles are congruent: side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA).
2. The SSS postulate states that if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
3. The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
4. The ASA postulate states that if two angles
Golden spiral sublime
This presentation discusses the construction of the golden spiral from the sublime triangle. It begins by introducing the sublime triangle, which is made up of sides from a regular pentagon. It then demonstrates how to construct the golden spiral by repeatedly drawing angle bisectors to generate similar, smaller triangles and using the points to lay out concentric arcs that form the spiral shape. The presentation provides step-by-step instructions on drawing the angle bisectors, finding the points, and using the points and radii to construct the golden spiral arcs.
DIGITAL TEXT BOOK
This document contains a chapter from an 8th grade mathematics textbook on the topic of equal triangles. It discusses several properties of equal triangles, including:
1) If the sides of one triangle are equal to the sides of another triangle, then the angles of the triangles are also equal.
2) If one side of a triangle and the angles at its ends are equal to one side of another triangle and the angles at its ends, then the third angles are also equal and the sides opposite equal angles are equal.
3) In any parallelogram, the diagonals bisect each other and the point of intersection is the midpoint of both diagonals.
Triangle
This document provides information about different types of triangles categorized by side lengths, angle measures, and combinations of sides and angles. It defines equilateral, isosceles, scalene, right, acute, and obtuse triangles. Examples are given to illustrate each type. Formulas for calculating the perimeter and area of triangles are presented. Exercises are included for the student to practice determining perimeters, areas, and drawing different triangle types.
Triangles For Class 10 CBSE NCERT
The document describes how to determine if three lines will form a triangle based on their lengths. It states that if the sum of the lengths of the two shortest lines is less than the longest line, the lines will not form a triangle. If the sum is equal to the longest line, the two shortest lines will overlap the longest line. Only if the sum is greater than the longest line will the three lines form a triangle.
Quadrilateral notes
The document discusses determining what type of quadrilateral a shape is on a coordinate plane. It reviews properties of different quadrilaterals and provides steps to systematically check if a shape is a trapezoid, parallelogram, rectangle, square, or just a quadrilateral. The document then works through determining the type of quadrilateral formed by the points A(-4, -2), B(-2, 4), C(4, 2), D(2, -4) by checking properties such as parallel sides, perpendicular sides, and side lengths. Through this process, it is proven that the shape is a square.
Triangles
Triangles have three non-collinear points called vertices and three segments connecting them called sides. A triangle is named by listing its three vertices, usually in clockwise order. Triangles are classified based on sides as equilateral, isosceles, or scalene and based on angles as acute, right, obtuse, or equiangular. The sum of the interior angles of any triangle is always 180 degrees. Exterior angles of a triangle are supplementary to their adjacent interior angles.
Geometry the congruence of triangles
The document discusses congruent triangles and different postulates that can be used to prove triangles are congruent. It states that triangles can be proved congruent without showing all three pairs of congruent sides and angles. It then provides examples of different postulates like AAS, SAS, and SSS that can be used to prove triangles congruent. It also discusses isosceles triangles and how if two isosceles triangles share a common base, the line segment joining their vertices will bisect the common base at a right angle.
Digit l textbook 131
This document provides information about congruent triangles. It defines congruent triangles as two triangles that have the same shape and size, with corresponding sides and angles being equal. It describes several triangle congruence theorems including SSS, SAS, ASA, AAS, and RHS, which establish that triangles are congruent if certain combinations of sides and/or angles are equal. It also discusses isosceles triangles, angle bisectors, and provides examples applying the congruence theorems to prove triangles are congruent or not.
7th pre alg similarity & triangles
This document discusses similarity between shapes and triangles. It provides the following key points:
1. Two shapes are similar if corresponding angles are equal and corresponding sides are proportional. All regular polygons and rectangles can be similar or not similar depending on if they meet these criteria.
2. If two shapes are similar, one is an enlargement of the other. The scale factor represents the ratio of corresponding sides.
3. Similar triangles only require equal corresponding angles, not proportional sides. Unknown sides of similar triangles can be found using scale factors determined from corresponding sides.
4. Parallel lines drawn to the sides of a triangle form similar triangles. This property can be used to solve problems involving similar triangles.
Lesson4
The document provides information on triangle basics, including definitions, naming conventions, angle properties, classifications based on angles and sides, special right triangles (45-45-90 and 30-60-90), and the Pythagorean theorem. Key points covered include: a triangle has three sides and three angles; the three angles of any triangle sum to 180 degrees; triangles can be classified as acute, right, or obtuse based on their angles or as equilateral, isosceles, or scalene based on their sides; special right triangles have predictable side ratios; and the Pythagorean theorem relates the sides of a right triangle.
Quadrilateral Family[1] Rashmi Kathuria
1) The document introduces students to different types of quadrilaterals including parallelograms, rectangles, trapezoids, and provides examples found in daily life.
2) Key properties of parallelograms, rectangles, rhombus, squares, and trapezoids are defined such as opposite sides being parallel, right angles, and equal or congruent sides.
3) A quiz is provided to test understanding of different quadrilateral types.
Teacher lecture
This document provides an introduction to congruent triangles and the different methods to prove triangles are congruent: SSS, SAS, and ASA. It includes examples of using side and angle correspondences to show triangles are congruent according to the three congruence rules. Students are asked to complete a KWL chart on triangles as an exit ticket.
E-RESOUCE BOOK
The document contains information about triangles, including:
1) If two triangles have proportional sides and equal angles, they are similar triangles.
2) In a right triangle, a perpendicular line from the right angle to the hypotenuse divides it into two right triangles that are similar to each other and to the original triangle.
3) A line dividing two sides of a triangle proportionally is parallel to the third side.
Slm understanding quadrilaterals MATHS topic....
understanding quadrilateral is an MATHS topic through which you can explore, learn an dunderstand Quadrilateral.
Similar Triangles PPT and examples.ppt
The document discusses proportion and similar triangles in geometry. It defines proportion as an equation stating that two ratios are equal, and provides examples of using cross products to check for proportion. It then defines similar polygons and triangles as those with congruent corresponding angles and proportional corresponding sides. The document provides different methods to prove triangles are similar, including SAS, SSS, and AA similarity. It also discusses how corresponding parts of similar triangles, such as perimeters, altitudes, angle bisectors, and medians are proportional. Several theorems and examples involving parallel lines cutting across triangles proportionally are presented.
classification of quadrilaterals grade 9.pptx
This document defines and compares different types of quadrilaterals: parallelograms, rhombi, rectangles, squares, trapezoids, and kites. It provides properties and examples of each shape. Key points include: a parallelogram has two pairs of parallel opposite sides; a rhombus is a parallelogram with four congruent sides; a rectangle is a parallelogram with four right angles; a square has properties of both a rectangle and rhombus; a trapezoid has at least one pair of parallel sides; and a kite has two pairs of congruent consecutive sides. The document also covers angle sums, using properties to solve problems, and includes a logo
Triangles (Similarity)
The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.
Geomentry 2022.pptx
Geometry is a branch of mathematics that studies shapes, sizes, and spatial relationships. It arose from practical problems in surveying. Geometry covers topics like points, lines, planes, angles, triangles, similarity, trigonometry, quadrilaterals, transformations, and area. The document also provides tips on solving geometry problems and 15 multiple choice geometry questions with answers.
Similar to Area (20)
Congruence of Triangle 1.pptx Maths, Triangles for GRADE 8
Congruence of Triangle 1.pptx Maths, Triangles for GRADE 8
Recently uploaded
Community pharmacy- Social and preventive pharmacy UNIT 5
Covered community pharmacy topic of the subject Social and preventive pharmacy for Diploma and Bachelor of pharmacy
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
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/y977uz6bpd3af4qsebv7r9b7s21935vdWalmart 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!"
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
PCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Aberdeen
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Recently uploaded (20)
Community pharmacy- Social and preventive pharmacy UNIT 5
Community pharmacy- Social and preventive pharmacy UNIT 5
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
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...
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
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
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Area
- 2. Can you find the areas of figures? 6cm 3cm 4cm 4cm 2cm 5cm 4cm 3cm
- 3. A B PD C Q Area of Triangle The area of the triangle ∆ABP = — x AB x PQ = — x AB x CB = — x Area of rectangle ABCD 1 2 1 2 1 2
- 5. M1 M2 A B RRQP ‘Triangle with same base and between the same parallels are of equal area’
- 6. ‘Triangle with same base and between the same parallels are of equal area’
- 7. APPLICATION OF THIS THEOREM Can we draw a triangle with the same area as the triangle ABC shown below, but with the angle at A, aright angle? C BA
- 8. C BA D Here ∆ ABD is the required triangle
- 9. Try it also.. o Draw ∆ ABC with AB = 4cm, BC = 5cm and CA =6cm Draw an isosceles triangle of same area with one side as AB itself. o Draw ∆ ABC as in the above problem. Draw triangle of same area with two of its sides 6cm and 7cm.
- 10. Thank you Basil Roy Idiculla Mathematical science Mount Tabor Training College Pathanapuram