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4.2  Apply Congruence and Triangles

4.2  Apply Congruence and Triangles. A. P. R. B. Q. C. Congruent shapes. Corresponding sides are congruent Corresponding angles are congruent ABC  PQR Important to list corresponding angles in the same order. 5 cm. 5 cm. 4 cm. 7 cm.

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4.2  Apply Congruence and Triangles

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  1. 4.2 Apply Congruence and Triangles

  2. A P R B Q C Congruent shapes • Corresponding sides are congruent • Corresponding angles are congruent • ABC  PQR • Important to list corresponding angles in the same order

  3. 5 cm 5 cm 4 cm 7 cm

  4. Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. The diagram indicates that JKL TSR. Corresponding angles J T,∠ K S,L R Corresponding sides JK TS,KL SR,LJ RT EXAMPLE 1 Identify congruent parts SOLUTION

  5. Third Angles TheoremIf two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. A D B F C E

  6. FindmBDC. SOLUTION AB and ADCBCD, so by the Third Angles Theorem, ACDBDC. By the Triangle Sum Theorem, m ACD = 180°– 45° – 30°= 105° . So, mACD =mBDC = 105° by the definition of congruent angles. ANSWER EXAMPLE 4 Use the Third Angles Theorem

  7. Can the two figures be proven congruent? Explain.

  8. Can the two figures be proven congruent?

  9. Can the two figures be proven congruent? Explain.

  10. x = 17 y = 17

  11. A#29:Page 228#3 – 21 And #26

  12. Day 5 HWpg. 221 #1 -19, 21 – 37 pg. 228 #4 – 10, 19 -21, 26

  13. a = 9 b = 8

  14. Solve for “x” A D 45° 55° (2x+20)° B F C E

  15. Write a proof. GIVEN AD CB,DC AB CADACB ACDCAB, ACDCAB PROVE Use the Reflexive Property to show that AC AC. Use the Third Angles Theorem to show that BD EXAMPLE 5 Prove that triangles are congruent Plan for Proof

  16. Homework Day 5 Page 221 # 1 -19, 21 – 37 Page 228 # 4 -17, 19 – 21, 26

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