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Exploring Congruent Triangles

This lesson explores congruent triangles, focusing on their sides and angles, and the conditions for triangle congruence. It covers concepts such as corresponding parts and congruence statements, emphasizing the importance of identifying congruent angles and sides. Students will learn how transformations like translation, rotation, and reflection preserve triangle congruence. The activities include solving for unknowns in congruent triangle scenarios and forming congruence statements based on given information. This foundational knowledge is essential for advancing in geometry.

kevin-long
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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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