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Chapter 4

Chapter 4. 4.2 Congruence & Triangles. Objectives/Assignment. Identify congruent figures and corresponding parts Prove that two triangles are congruent Assignment: 1-29 all, quiz page 210. Goal 1: Identifying Congruent Figures.

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Chapter 4

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  1. Chapter 4 4.2 Congruence & Triangles

  2. Objectives/Assignment • Identify congruent figures and corresponding parts • Prove that two triangles are congruent • Assignment: 1-29 all, quiz page 210

  3. Goal 1: Identifying Congruent Figures • Two geometric figures are congruent if they have exactly the same size and shape. • When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

  4. ABC =̃ PQR B Q C P R A What are the corresponding angles? What are the corresponding sides? A & P B & Q C & R AB & PQ BC & QR CA & RP

  5. 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.

  6. Goal 2: Proving Triangles are Congruent • Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN R N 92o Q 92o M P

  7. Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN Statements Reasons 1.seg RP  seg MN 1. given seg PQ  seg NQ seg RQ  seg MQ 2. mP=mN 2. trans. prop = 3. P N 3. def of s 4. RQP MQN 4. vert s thm 5. R M 5. 3rds thm 6. ΔRQP Δ MQN 6. def of  Δs

  8. Theorem 4.4: Properties of Congruent Triangles • Reflexive Property of Congruent Triangles: Every triangle is congruent to itself • Symmetric Property of Congruent Triangles: If ABC =̃ DEF, then DEF =̃ ABC • Transitive Property of Congruent Triangles: If ABC =̃ DEF and DEF =̃ JKL, than ABC =̃ JKL

  9. Practice Problems • Name the congruent figures • Given M =̃ G and P =̃ H, find the value of x. E B D A C F (2X-50)° H M 142° N J P G 24°

  10. More Practice Problems Given that N =̃ R and L =̃ S, find the value of x. Given that LMN =̃ PQR, answer the following: mP= QR =̃ mM= LN =̃ mR= mN= R M S (2X+30)° N 55° 65° L T P N Q 45° R L 105° M

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