4.2: Congruence and Triangles

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Presentation transcript:

4.2: Congruence and Triangles GEOMETRY: Chapter 4 4.2: Congruence and Triangles

In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. In congruent polygons, this means that the corresponding angles and the corresponding sides are congruent.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 225.

Congruence Statements To express that two figures are congruent, use the congruent symbol,  , and list the corresponding vertices in the same order. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 225.

Ex. 1. Write a congruence statement for the triangles shown Ex. 1. Write a congruence statement for the triangles shown. Identify all pairs of congruent corresponding parts. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.

Ex. 1. Write a congruence statement for the triangles shown Ex. 1. Write a congruence statement for the triangles shown. Identify all pairs of congruent corresponding parts. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.

Find the value of x. (5) Find the value of y. (12) Ex. 2. In the diagram, ABCD  FGHK. Find the value of x. (5) Find the value of y. (12) Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 226.

Ex. 3: Maggie took the piece of fabric STUV shown in the diagram and cut it on the diagonal to make a scarf for her and a friend. Are the two pieces the same size and shape? Explain. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.

Theorem 4.3: Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.

Ex. 4: Find m  YXW. 1050 Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 227.

Theorem 4.4: Properties of Congruent Triangles Reflexive Property of Congruent Triangles For any triangle ABC, Symmetric Property of Congruent Triangles Transitive Property of Congruent Triangles Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 228.