# Identify Similar Triangles with Proofs Worksheets

How to Identify Similar Triangles with Proofs - Similar figures are those that have the same shape but different sizes. We can easily identify similar triangles by applying three similarity theorems specific to triangles. These three theorems involve, side-angle -side (SAS), Angle- Angle (AA), and Side-Side-Side (SSS). The three similarity theorems of a triangle depend upon the corresponding parts. That means that you take the measurements of one triangle and compare the same with the other triangle. You can also develop ratios of lengths, and if ratios are congruent, then corresponding sides are similar. Moreover, you need to consider the included angle while comparing the lengths or ratio of lengths of two triangles. Angle-Angle (AA) Theorem - Angle-Angle (AA) theorem says that two triangles are similar if the two pairs of their corresponding angles are congruent. These two triangles might appear as identical. To establish two triangles as congruent using this theorem, you only have to compare the two pairs of corresponding angles. Side-Angle-Side (SAS) Theorem - This theorem follows the order of a side, an included angle, and then a side. The SAS theorem says that two triangles are similar if two sides of a triangle are proportional to the two corresponding sides of second triangles, and the included angles are congruent. Side-Side-Side (SSS) Theorem - The last theorem telling us about the congruency of a triangle, states that if all three sides of one triangle are proportional to all three corresponding sides of the second triangle, then those two triangles are congruent.

• ### Basic Lesson

Introduces students to use proofs with similar triangles. Identical triangles are similar. Mathematically, similar triangles have both corresponding angles equal, while the lengths of the corresponding sides are in proportion.

• ### Intermediate Lesson

Guides students through using proofs to find sides of triangles.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of similar triangles. Identify the similar triangles in each figure. Explain why they are similar and use the given information to answer the following sets of questions.

• ### Independent Practice 2

Students tackle 20 similar triangles problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to understand the concepts of Identify Similar Triangles with Proofs.

• ### Skill Quiz

This tests the students ability to understand Identify Similar Triangles with Proofs.

• ### Answer Key

Answers for the homework and quiz.

• ### Answer Key Part 2

Answers for lessons and both practice sheets.

#### The Pythagorean Theorem states,

"In a right triangle, the square of the hypotenuse equals the sum of the squares of the 2 other sides." Other civilizations knew it long before Pythagoras, but he generalized it and made it popular.