Chapter 4.2 Notes: Apply Congruence and Triangles

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Presentation transcript:

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.

Identifying congruent figures Two geometric figures are congruent if they have exactly the same size and shape. NOT CONGRUENT CONGRUENT

Triangles Corresponding angles A ≅ P B ≅ Q C ≅ R Corresponding Sides AB ≅ PQ BC ≅ QR CA ≅ RP B Q R A C P

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. 3 Using the Third Angles Theorem Find the value of x. In the diagram, N ≅ R and L ≅ S. From the Third Angles Theorem, you know that M ≅ T. So mM = mT. From the Triangle Sum Theorem, mM=180° - 55° - 65° = 60° mM = mT 60° = (2x + 30)° 30 = 2x 15 = x (2x + 30)° 55° 65°

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 .