Warm Up 1. Name all sides and angles of ∆FGH.

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Presentation transcript:

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?

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

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

CPCTC Corresponding Parts of Congruent Triangles are Congruent.

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

EXAMPLE 1 Identify congruent parts Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

Complete each congruence statement.

Write a congruence statement.

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.

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.

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

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

1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. 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  ____