Congruence Of Triangle
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This document discusses congruence of triangles in mathematics. It defines congruence as two shapes being equal in shape, size, and area or coinciding exactly when placed on top of each other. There are five criteria for triangle congruence: side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS). Each rule states that if the given sides or angles are equal, then the triangles are congruent. Examples are provided to illustrate each rule.
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This document discusses similarity and congruency of triangles. It defines similarity as two polygons having equal corresponding angles and proportional corresponding sides. Congruency requires equal corresponding sides and angles. The document outlines three criteria for similarity: AAA, SSS, and SAS. It also covers the basic proportionality theorem, areas of similar triangles being proportional, and how Pythagoras' theorem relates to right triangles being similar.
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This document discusses several geometry theorems:
- The Basic Proportionality Theorem (also known as Thales' Theorem) states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
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The document discusses different criteria for determining similarity and congruence of triangles:
1) AA and SSS criteria state that triangles are similar if corresponding angles or sides are proportional.
2) SAS criterion states triangles are congruent if two sides and the included angle are equal.
3) SSS, ASA, and HL criteria also determine triangle congruence if three sides, two angles and included side, or hypotenuse and leg are equal.
The document also discusses scale factors in similar figures and angle relationships formed by parallel lines cut by a transversal.
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This document summarizes key concepts in geometry related to triangles. It discusses similarity criteria including AAA, SSA, and SSS. It also covers the area theorem, Pythagorean theorem, and its converse. The basic proportionality theorem and its converse are explained as well as how they relate to parallel lines. In summary, this document outlines important triangle properties and theorems for understanding similarity, area, right triangles, and parallel lines.
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This document discusses different methods for proving that triangles are congruent: SSS, SAS, ASA, AAS, and HL. It defines congruent polygons as having the same size and shape, meaning all corresponding sides are the same length and all corresponding angles have the same measure. The order of letters in a congruence statement indicates which angles or sides are being shown as congruent to prove the triangles are congruent.
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The document discusses different types of triangles based on the lengths of their sides: equilateral triangles have all three sides equal; isosceles triangles have two equal sides; scalene triangles have no equal sides. It also describes criteria for determining if two triangles are congruent, including side-angle-side (SAS), angle-side-angle (ASA), and side-side-side (SSS). Properties of triangles are outlined, such as the angle sum property that the interior angles sum to 180 degrees and the exterior angle property relating an exterior angle to the two interior angles. The Pythagorean theorem relating the sides of a right triangle is presented along with Heron's formula for calculating the area of any triangle.
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This document discusses different rules for determining if two triangles are congruent:
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- SAS (Side-Angle-Side) rule says two triangles are congruent if two sides and the angle between them are equal.
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Triangles are congruent if their corresponding angles and sides are equal. There are three postulates for triangle congruency: SSS (side-side-side), ASA (angle-side-angle), and SAS (side-angle-side). SSS states that if all three sides of one triangle are equal to those of another, the triangles are congruent. ASA states that if two angles and the included side of one triangle are equal to those of another, the triangles are congruent. SAS states that if a side and the included angle of one triangle are equal to those of another, the triangles are congruent.
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This document discusses triangle congruence postulates and theorems. It introduces three main postulates: SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and SSS (Side-Side-Side). SAS states that if two sides and the included angle of one triangle are congruent to those of another, the triangles are congruent. ASA states the same for two angles and the included side. SSS states that if all three sides of one triangle are congruent to those of another, the triangles are congruent. The document provides examples and exercises applying these postulates.
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This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
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1. Two triangles are congruent if their corresponding sides and angles are equal. This can be determined through Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), Side-Side-Side (SSS), or Right-Angle-Hypotenuse-Side (RHS) criteria.
2. Triangles have properties related to equal sides and angles, including that angles opposite equal sides are equal, and sides opposite equal angles are equal.
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This document discusses triangle congruence theorems. It explains that triangles can be proven congruent in different ways beyond just having three pairs of congruent sides and angles. The main triangle congruence theorems covered are: SAS, SSS, ASA, AAS, HL, HA, LL, and LA. It provides examples applying these theorems to determine if pairs of triangles are congruent. The document also addresses right triangles and the additional theorems used to prove those congruent: HL, HA, LL, and LA.
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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.
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This document discusses different theorems for proving triangles are congruent:
- Side-Side-Side (SSS) - If three sides of one triangle are congruent to three sides of another, the triangles are congruent.
- Side-Angle-Side (SAS) - If two sides and the included angle of one triangle are congruent to those of another, the triangles are congruent.
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This document discusses congruency in triangles. It defines congruent triangles as those that are the same size and shape. There are five conditions that can be used to determine if two triangles are congruent: side-side-side, side-angle-side, angle-side-angle, angle-angle-side, and right-hypotenuse-side. These conditions show the minimum information needed to determine if all angles and side lengths are the same between two triangles. The document provides examples of applying each condition and includes practice problems for the reader.
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Es una presentación del Profesor Jim Smith sobre congruencia de triángulos muy didáctica. Viene en idioma inglés.
Ppt on triangles class x made my jatin jangid
The document discusses learning objectives related to similarity of triangles. Students will understand the concept of similarity, prove and apply the Basic Proportionality Theorem, learn similarity rules like SAS, SSS, and AA, and learn and apply Pythagoras' Theorem and its converse. It also defines similar figures as those with the same shape but not necessarily the same size, and discusses how similarity can be used to indirectly measure distances like the height of Mount Everest.
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Two triangles are congruent if their sides and angles are equal. There are four criteria for determining if triangles are congruent:
1) Side-Side-Side (SSS): If all three sides of one triangle are equal to the corresponding sides of another triangle.
2) Side-Angle-Side (SAS): If two sides and the included angle of one triangle are equal to those of another triangle.
3) Angle-Side-Angle (ASA) or Angle-Angle-Side (AAS): If two angles and the included side of one triangle are equal to those of another.
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Congruence Of Triangle
- 1. Mathematics Activity On the Congruence of Triangles
- 2. What is congruence in Maths? Two or more shapes, lines etc. when equal in every aspect be it shape, size or area, or when two shapes placed on top of each other exactly coincide with one another, are called congruent shapes These two rectangles are congruent
- 3. Criteria for Congruence of Triangle SSS Congruence rule: When all the sides of both the triangles are congruent, both the triangles are equal. SAS Congruence rule: When any two sides and the included angle (angle between the two sides) are congruent for both the triangles, they are congruent. AAS Congruence rule: Two triangles are congruent when any two pairs of angles and a corresponding sides are equal ASA Congruence rule: When two angles and the included side are equal for two triangles, then both the triangles are congruent RHS Congruence rule: In a right-triangle when the hypotenuse and any one side is equal, both the triangles are congruent.
- 4. SSS Congruence Rule SSS Side-Side-Side Side AB = PQ Side BC = QR Side CA = RP Therefore ABC is Congruent to PQR A B C P Q R
- 5. SAS Congruence Rule SAS Side Angle Side Side AB=PQ Side CA=QP Angle A = P ABC is Congruent to PQR A B C Q P R
- 6. AAS Congruence Rule ASA Angle-Angle-Side A = P B = Q Side CA = RS ABC is Congruent to PQR A B C Q P R
- 7. ASA Congruence Rule ASA Angle-Side-Angle A = P B = Q Side AB = PQ ABC is Congruent to PQR A B C Q P R
- 8. RHS Congruence Rule RHS Right angle-Hypotenuse-Side B = Q = 90 Side AB = PQ (or) Side BC = QR Side (Hypotenuse) CA = RP ABC is Congruent to PQR A CB P R Q