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Chapter 4

Learn about congruent figures in geometry and how to identify corresponding angles and sides. Understand the Third Angles Theorem and Properties of Congruent Triangles, and practice proving triangles are congruent. Solve practice problems to reinforce your understanding.

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Chapter 4

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  1. Chapter 4 4.2 Congruence & Triangles

  2. 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.

  3. 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

  4. 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.

  5. 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

  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 mP=92o & mN is 92o 2. mP=mN 2. trans. prop = 3. P N 3. def of s 4. RQP MQN 4. vertsthm 5. R M 5. 3rdsthm 6. ΔRQP Δ MQN 6. def of  Δs

  8. 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°

  9. 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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