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## Triangle Similarity

## Contents |

## **Triangle Similarity**

Triangles can be proven similar by three different ways; angle-angle similarity, side-angle-side similarity, and side-side-side similarity. This page is designed to help students discover these relationships and why they allow us to say two or more triangles are similar and not have to prove every time that all corresponding angles are congruent and all corresponding sides are proportional.

### Triangle AA~

Angle-Angle similarity states that if we have two angles of two triangles congruent, then the two triangles are similar. The following dynamic worksheet allows students to see that by having two angles congruent, the triangles will always be similar.

### Triangle SAS~

Side-Angle-Side similarity states that if we have an angle of one triangle congruent to the angle of another triangle and the included corresponding sides are proportional, then the triangles are similar. The following dynamic worksheet allows students to see that by having these two sides proportional and angle congruent, the two triangles will be similar.

### Triangle SSS~

Side-Side-Side similarity states that if we have all three sides of one triangle proportional to the corresponding sides of another triangle, then the two triangles are similar. The following dynamic worksheet allows students to discover that when they do have these corresponding sides proportional, then the triangles are similar

(Note: This one is the hardest of the three. To get all three sides in the same ratio takes time. If you are unable to achieve the same ratios make note that the closer you get to having all the ratios the same, the closer the angles are to being congruent.)

### Right Triangle Similarity

This is where you make a conjecture about what the altitude to the hypotenuse of a right triangle creates with the right triangle.

Created By Jacob Dunklee