Congruent Triangles

1. Congruent Triangles Notes 17 – Section 4.3

2. Essential Learnings • Students will understand and be able to name and use corresponding parts of congruent triangles. • Students will be able to prove congruence of triangles.

3. Congruent Polygons • Two polygons are congruent if and only if their corresponding parts are congruent. Corresponding Angles A  J B  K C  L Corresponding Sides AB  JK BC  KL AC  JL Congruence Statement ABC  JKL B J C A L K

4. Congruence Statements • Valid congruence statements for congruent polygons list corresponding vertices in the same order. Valid Statement:ABC  JKL Not a Valid Statement: ACB  LJK

5. Example 1 Show that the polygons are congruent by identifying congruent corresponding parts. Then write a congruence statement. Congruence Statement: ABC ≅ ________ Z A X Y C B

6. Example 2 Show that the polygons are congruent by identifying congruent corresponding parts. Then write a congruence statement. Congruence Statement: Polygons _______ ≅ ________ A B Y Z D C X W

7. Third Angles Theorem • If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. C A E B D F

8. Properties of Triangle Congruence • Reflexive Property: ABC  ABC • Symmetric Property: If ABC  JKL, then JKL  ABC • Transitive Property: If ABC  JKL and JKL  RST , then ABC  RST

9. Example 3 Polygon LOVE  polygon MATH. Find each variable. mL=8x+48, mE=15z, OV=3y, EV=3w+5, mH=12z+15, mM=15x+20, AT=18, TH=4w+2 L T H O E A V M

10. Example 3 cont. Polygon LOVE  polygon MATH. Find each variable. mL=8x+48, mE=15z, OV=3y, EV=3w+5, mH=12z+15, mT=15x+20, AT=18, TH=4w+2 L T H O E A V M

11. Example 4 Draw and label a figure to represent the congruent triangles. Then find x and y. LMN  RST, mL=49, mM=10y, mS=70, mT=4x+9

12. Assignment Pages 257-259: 9, 11, 13-16, 19, 29 Mastery Assignment Due at the end of ICE tomorrow! Quiz on Friday! Math’s Mate 2-1 Unit Study Guide 3