Chapter 5 Congruent Triangles

Section 5 Using Congruent Triangles

If you know that two triangles are congruent, you can use the definition of congruent triangles from Lesson 5.1 to conclude that the corresponding parts are congruent. If you know ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹, then you can conclude:

Example 1: Use Corresponding Parts In the diagram, AB and CD bisect each other at M. Prove that <A ≅ <B. Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5) 6) 6)

Diagrams often show overlapping triangles Diagrams often show overlapping triangles. It is usually helpful to visualize or redraw the triangles so that they do not overlap.

Example 2: Visualize Overlapping Triangles Sketch the overlapping triangles separately. Mark all congruent angles and side. Then tell what theorem or postulate you can use to show ∆𝐽𝐺𝐻≅∆𝐾𝐻𝐺.

Example 3: Use Overlapping Triangles Write a proof that shows AB ≅ DE Example 3: Use Overlapping Triangles Write a proof that shows AB ≅ DE. Statements Reasons 1) 1) 2) 2) 3) 3) 4) 4) 5) 5)

Checkpoint: Use Overlapping Triangles 1) Tell which triangle congruence theorem or postulate you would use to show that AB ≅ CD.

Checkpoint: Use Overlapping Triangles Redraw the triangles separately and label all congruences. Explain how to show that the triangles or corresponding parts are congruent. 2) 3)

EXIT SLIP