The following worksheets give your students a review of using proofs to identify similar triangles.

#### How Do Prove the Similarity of Triangles? Similar figures are defined as geometric figures that have the same shape but different sizes. Typically, we use three theorems to establish the similarity of the triangles. The three theorems involved are, side-angle -side (SAS), Angle- Angle (AA), and Side-Side-Side (SSS). Angle-Angle (AA) Theorem - Angle-Angle (AA) theorem says that two triangles are similar if the two pairs of their corresponding angles are congruent. They might appear as identical. To establish them 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.

In triangle geometry we are often trying to prove that two or more triangles are similar. If they are similar they are not the same exact, but their corresponding angles and sides are in proportion to each other. We can prove similarity using a number of different methods and it is all situational based. We can use the Angle-Angle Similarity Postulate if both triangles have a two pairs of congruent angles. If the lengths of corresponding sides of the triangles are proportional, we can use the Angle-Angle Similarity Postulate. If they share a congruent angle and the corresponding legs of that angle are equal in length, we can use the Side-Angle-Side Similarity Theorem. These worksheets explains how to determine if triangles and similar and how to use similarity to solve problems. Your students will use these activity sheets to identify similar triangles by applying the correct proofs, as well as calculate segment lengths. Students should already be familiar with the applicable proofs and formulas.

# Print Similarity of Triangles Proofs Worksheets

## Similar Proofs Lesson

This worksheet explains how to determine if a given pair of triangles is similar. A sample problem is solved, and two practice questions are provided.

## Worksheet

Students will determine if a given pair of triangles is similar. Ten questions are provided.

## Similar Proofs Practice

Using the information provided, students will determine if there is a high degree of similarity Ten questions are provided.

## Review and Practice

This worksheet review how to determine if a given pair of shapes are similar. Six practice questions are provided.

## Quiz

Students will demonstrate their proficiency stating if a given pair of figures share a similarity Ten problems are provided.

## Skill Check

Students will work this skill one more time. Space is included for students to copy the correct answer when given.

## Similarity of Triangles in Numeric Problems Lesson

This worksheet explains how to use the similarity of triangles to find the length of a side. A sample problem is solved, and two practice questions are provided.

## Numeric Problems Worksheet

Students will find the length of a side of a triangle using similarity. Ten questions are provided.

## Practice

Students will use the similarity of triangles to find the length of a side. Ten questions are provided.

## Review and Practice

This worksheet reviews how to use the similarity of triangles to find the length of a side. Six practice questions are provided.

## Quiz

Students will demonstrate their proficiency using the similarity of triangles to solve problems. Ten problems are provided.

## Skills Check

Students will use the similarity of triangles to find the length of a side. Three questions are provided, and space is included for students to copy the correct answer when given.

## Identify Similar Triangles with Proofs: Lesson

Identical triangles are similar. Mathematically, similar triangles have both corresponding angles equal, while the lengths of the corresponding sides are in proportion.

## Worksheet 1

Use the skills that we have covered, so far, to answer each of the problems.

## Worksheet 2

Find mixed portions of various triangles using geometry.

## Review Sheet

Determine if the triangles are similar through proofs.

## Quiz

Prove that two triangles are similar.

## Check Up Sheet

Find the ratio m <MGN / m <EGB, FIND MG and EN.

### Here Is Another Approach For You To Consider

We will have two similar triangles when their corresponding sides are in proportion and their same angles are congruent. We have to use different methods to prove congruent triangles and similar triangles. We can use the following process for proving triangles similar. Two angles are congruent to the other two corresponding angles of the other triangle. It would be sufficient to show this condition to prove two triangles similar. The triangle's two angles are congruent to the same angles of another triangles, they are similar. If angle A is congruent to angle D and angle B is congruent to angle E. Then, you have to prove triangle ABC ~ triangle DEF. You will need to solve transformational proof and research for the accurate sequence of transformations that you can map out triangle ABC onto the triangle DEF. We will use the following method to prove triangle congruent. In can only happen when you show three group of corresponding sides in proportion. The condition will be AB/DE = BC/ EF = AC/DF. Then, you will have to find triangle ABC similar to triangle DEF. You can also prove triangles are similar when two groups of corresponding sides are in proportion and the angles, they add are congruent. So, the condition will be AB/DE = AC/DF and angle A is congruent to angle D. Then, triangle ABC is similar to the triangle DEF.