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Congruent Triangles

Congruent Triangles. Notes 17 – Section 4.3. 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. Congruent Polygons.

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Congruent Triangles

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  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

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