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Chapter 4 Section 3

Chapter 4 Section 3. Exploring Congruent Triangles. Warm-Up. P. K. B. 1) Find m<ACB 2) Find m<CLK 3) Find m<CBP 4) Which two angles are the remote interior angles for <MLK? 5) Find m<BCK 6) Find m<MLK. 42. 42. 70. 70. A. C. L. M. Warm-Up. P. K. B. 1) Find m<ACB

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Chapter 4 Section 3

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  1. Chapter 4Section 3 Exploring Congruent Triangles

  2. Warm-Up P K B • 1) Find m<ACB • 2) Find m<CLK • 3) Find m<CBP • 4) Which two angles are the remote interior angles for <MLK? • 5) Find m<BCK • 6) Find m<MLK 42 42 70 70 A C L M

  3. Warm-Up P K B • 1) Find m<ACB • All the angles in a triangle add up to 180. • 180 = 70 + 42 + m<ACB • 180 = 112 + m<ACB • 68 = m<ACB • 2) Find m<CLK • The third angle theorem states if two angles in a triangle are congruent to two angles in another triangle, then the thirds angles are also congruent.  • Since both triangles have angles measuring 42 and 70, m<ACB is congruent to m<CLK. • M<ACB = 68 = m<CLK 42 42 70 70 A C L M

  4. Warm-Up P K B • 3) Find m<CBP • <CBP and <ABC are supplementary. • 180 = m<CBP + m<ABC • 180 = m<CBP + 42 • 138 = m<CBP • 4) Which two angles are the remote interior angles for <MLK? • <LKC and <LCK 42 42 70 70 A C L M

  5. Warm-Up P K B • 5) Find m<BCK • <ACB, <BCK, and <KCL are supplementary. • 180 = m<ACB + m<BCK + m<KCL • 180 = 68 + m<BCK + 70 • 180 = 138 + m<BCK • 42 = m<BCK • 6) Find m<MLK • The exterior angle theorem states that the remote interior angles add up to the exterior angle. • m<MLK = m<LKC + m<LCK • m<MLK = 42 + 70 • m<MLK = 112 42 42 70 70 A C L M

  6. Vocabulary • Congruent Triangles-Triangles that are the same size and same shape. • CPCTC-Two Triangles are congruent if and only if their corresponding parts are congruent. • Congruence Transformations- If you slide, rotate, or flip a figure, congruence will not change. • Theorem 4-4- Congruence of triangles is reflexive, symmetric, and transitive. • * Use to indicate each correspondence.

  7. Example 1: If Triangle ABC is congruent to Triangle DEF, name the corresponding congruent angles and sides. B E A D C F AB DE BC EF AC DF <A <D <B <E <C <F

  8. Example 2: If Triangle RPQ is congruent to Triangle ZYX, name the corresponding congruent angles and sides. P X Y Q Z RP ZY PQ YX RQ ZX <R <Z <P <Y <Q <X R

  9. Example 3: If Triangle BIG is congruent to Triangle DEN, name the corresponding congruent angles and sides. Draw a figure and mark the corresponding parts. B BI DE IG EN BG DN <B <D <I <E <G <N I G D N E

  10. Example 4: If Triangle PQRis congruent to Triangle RST, name the corresponding congruent angles and sides. Draw a figure and mark the corresponding parts. T P PQ TS QR SR RR TR <R <T <Q <S <R <R Q S R

  11. Example 5: Complete the congruence statement. T Triangle TRV is congruent to _________. Triangle DEG B) Triangle XYZ is congruent to __________. Triangle PVZ C) Triangle YZW is congruent to __________. Triangle WXY R V D X P G E V Y X Y Z W Z

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