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Chapter 4.2 Notes: Apply Congruence and Triangles

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

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Chapter 4.2 Notes: Apply Congruence and Triangles

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

  2. 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.

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

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

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

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

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

  8. 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.

  9. 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 Ex. 3 Using the Third Angles Theorem (2x + 30)° 55° 65°

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

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

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

  13. 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 .

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