Tips For Proving Overlapping Triangles Congruent: Identify Common Segments And Angles, Use Congruence Theorems, Prove Congruence Using Congruent Parts, And Consider Additional Information.

What often helps when trying to prove overlapping triangles congruent?

redrawing the two triangles separately

When trying to prove overlapping triangles congruent, there are a few things that can often be helpful:

1. Identify common segments and angles: Look for segments or angles that are shared between the two triangles. If two triangles have the same segment or angle, it can be a good place to start in showing that the triangles are congruent.

2. Use congruence theorems: There are several congruence theorems that can be used to prove that two triangles are congruent. These include the Side-Side-Side (SSS) theorem, Side-Angle-Side (SAS) theorem, and Angle-Side-Angle (ASA) theorem. Determine if any of these theorems can be applied to the overlapping triangles.

3. Prove congruence using congruent parts: If two triangles have congruent sides or angles, they are said to have congruent parts. If you can prove that two pairs of corresponding angles or sides are congruent, you can use the Congruent Parts of Congruent Triangles are Congruent (CPCTC) theorem to show that the two triangles are congruent.

4. Consider additional information: If you are given additional information about the triangles, such as the lengths of certain segments or the measures of certain angles, you can use this information to help in your proof. Consider drawing auxiliary lines to create right angles or to divide triangles into smaller, more manageable shapes.

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