# G.3.9.2 How Many Pieces?

- Author:
- Katie Akesson

Below is triangle ABC.
Your task is to create a similar triangle to triangle ABC.
We've done an activity like this before when we were exploring congruent triangles.
The purpose of the activities below is to determine what is the

*least amount*of information you can use to construct a triangle that will be similar to the original triangle ABC. Once you have moved the sliders to fit the given criteria, try and move other parts of the triangle. After everyone has had a chance to make a triangle with the given criteria, we'll compare and calculate to see if the given information was enough to make everyone's triangles the*similar*to triangle ABC.__For this first drawing lets make just one angle measure congruent to the original triangle ABC.__

**Attempt #1**...one angle__Draw triangle__: angle

*DEF*with the given measures*DEF*= 82 degrees Move the green slider so that angle

*DEF*is 82 degrees; then see if you can move any other parts of the triangle. Is the triangle you constructed similar to the original triangle ABC?

__For second drawing lets make two angle measures congruent to the original triangle ABC.__

**Attempt #2**...two angles__Draw triangle__: angle

*DEF*with the given measures*DEF*= 82 degrees angle

*ACB*= 38 degrees Move the green slider so that angle

*DEF*is 82 degrees and move the purple slider so that angle ABC is 38 degrees; then see if you can move any other parts of the triangle. Is the triangle you constructed similar to the original triangle ABC?

Angle-Angle Triangle Similarity Theorem: In two triangles, if two pairs of corresponding angles are congruent, then the triangles must be similar. (Theorem)