Chapter 5 Congruent Triangles KEY TERMS  Corresponding parts  Congruent figures  Proof  Distance from a point to a line  Equidistant  Perpendicular bisector  Reflection  Line of symmetry

Chapter Readiness ANSWER D Vocabulary Check 1.Which segment in the figure is the hypotenuse? KL LN NMKM

ANSWER G Skill Check Chapter Readiness ANSWER D 25°50°90°100° 2. If m  FGH = 100° and GJ bisects  FGH, what is m  FGJ?  7  2  5  2  1  8  3  7 Use the diagram at the right to determine which of following statements is true. 3.

CORRESPONDING PARTS Congruence and Triangles Today’s Essential Questions:  How can I identify corresponding angles of congruent triangles?  How can I identify corresponding sides of congruent triangles?

Ex. 1 List Corresponding Parts Given that  JKL   RST, list all corresponding congruent parts.

Ex. 2Write a Congruence Statement The two triangles are congruent. a. Identify all corresponding congruent parts. b. Write a congruence statement.

Ex. 2 Write a Congruence Statement b.List the letters in the triangle names so that the corresponding angles match. One possible congruence statement is ∆ ABC  ∆ FDE.

Ex. 3 Use Properties of Congruent Triangles a. b. In the diagram, ∆ PQR  ∆ XYZ. Find the length of XZ. Find m  Q.

Checkpoint Listing Corresponding Parts Given ∆ STU  ∆ YXZ, list all corresponding congruent parts. 1.

Checkpoint Applying Corresponding Parts 2. Given ∆ABC  ∆ DEF, find the length of DF and m  B.

Checkpoint Which congruence statement is correct? Why? 3. A. ∆ JKL  ∆ MNP B. ∆ JKL  ∆ NMP C. ∆ JKL  ∆ NPM IDENTIFYING CORRECT CONGRUENCY STATEMENTS

Understand Triangles are congruent if their corresponding parts are congruent. That is, if all three sets of sides and angles are congruent, the triangles are congruent. Checking for Congruence

Ex. 4 Determine Whether Triangles are Congruent Use the two triangles shown below. a. Identify all corresponding congruent parts. b. Determine whether the triangles are congruent. If they are congruent, write a congruence statement.

Ex. 5 Determine If Triangles are Congruent In the figure, HG || LK. Determine whether the triangles are congruent. If so, write a congruence statement.

5.1 Discussion: Small Groups  p. 236 #1-13. Please discuss out loud.  Then solve #14-26 even.

Exit Slip Determine If Triangles are Congruent In the figure, XY || ZW. Determine whether the two triangles are congruent. If they are, write a congruence statement.