4-7 Congruence in Overlapping Triangles
Objectives
To identify congruent overlapping triangles
To prove two triangles congruent using other congruent triangles
In the Solve It, you located individual triangles among a jumble of triangles. Some triangle relationships are difficult to see because the triangles overlap.
Essential Understanding You can sometimes use the congruent corresponding parts of one pair of congruent triangles to prove another pair of triangles congruent. This often involves overlapping triangles.
Overlapping triangles may have a common side or angle. You can simplify your work with overlapping triangles by separating and redrawing the triangles.
Problem 1 Identifying Common Parts
What common angle do
Think
How can you see an individual triangle in order to redraw it?
Use your finger to trace along the lines connecting the three vertices. Then cover up any untraced lines.
Separate and redraw
The common angle is
✓ Got It?
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- What is the common side in
- What is the common side in
- What is the common side in
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs