Chapter 4.2 Notes: Apply Congruence and Triangles

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Chapter 4.2 Notes: Apply Congruence and Triangles Goal: You will identify congruent figures.

Two geometric figures are congruent if they have exactly the same size and shape. Congruence Statements 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 sides and the corresponding angles are congruent.

When you write a congruence statement for two polygons, always list the corresponding vertices in the same order. Congruence Statement: __________________ Corresponding angles: ___________________ Corresponding sides: ____________________

Ex. 1: Write a congruence statement for the triangles Ex.1: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

Ex.2: In the diagram, . a. Find the value of x. b. Find the value of y.

Ex. 3: In the diagram below,. a Ex.3: In the diagram below, . a. Identify all pairs of congruent corresponding parts. b. Find the value of x and find .

Ex.4: Show that . 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.

Ex.5: Find . Ex.6: In the diagram, what is ?

Ex. 7: The two triangles are congruent Ex.7: The two triangles are congruent. Identify all angles and sides that are congruent. Then write a congruence statement.

Ex.8: In the diagram, a. Find the value of x. b. Find the value of y.

Properties of Congruent Triangles Theorem 4.4 Properties of Congruent Triangles: Reflexive Property of Congruent Triangles: For any triangle ABC, . Symmetric Property of Congruent Triangles: If , then . Transitive Property of Congruent Triangles: If , then .