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Exploring Congruent Triangles

Exploring Congruent Triangles. Section 4.5. Warm Up 1. Name all sides and angles of ∆ FGH . 2. What is true about  K and  L ? Why? 3. What does it mean for two segments to be congruent?. F. B. A. C. E. D. The Idea of a Congruence.

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Exploring Congruent Triangles

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  1. Exploring Congruent Triangles Section 4.5

  2. Warm Up 1.Name all sides and angles of ∆FGH. 2. What is true about K and L? Why? 3.What does it mean for two segments to be congruent?

  3. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape. Each triangle is made up of six parts: 3 sides and 3 angles

  4. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

  5. Congruent Triangles CPCTC Corresponding Parts of Congruent Triangles are Congruent.

  6. Congruence Transformations • Congruency amongst triangles does not change when you… • slide (translation), • Turn (rotation), • or flip (reflection) … the triangles.

  7. 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

  8. Complete each congruence statement.

  9. Write a congruence statement.

  10. Given ΔBCD = ΔRST, m C = 57, m R = 64, m D = 5x + 4. Find x and m T. Given ΔQRS = ΔLMN, RS = 8, QR=14, QS=10, MN = 3x – 25. Find x.

  11. Name the corresponding angles and sides if ΔBCD = ΔEFG. Given ΔCAT = ΔDOG, CA=14, AT=18, TC=21 and DG=2x+7, find the value of x.

  12. mDBC. Given: ∆ABC ∆DBC. Find the value of x and

  13. Given: ∆ABC  ∆DEF Find the value of x. Find mF.

  14. Lesson Quiz 1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. Given that polygon MNOP polygon QRST, identify the congruent corresponding part. 2. NO  ____ 3. T  ____

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