Happy Wednesday math peeps! TIn today’s post, we are going to go over Proving Similar Triangles, by going over:

1) What it means when two triangles are similar?

2) How to prove two triangles similar?

3) How to find missing side lengths given triangles are similar?

For even more practice, don’t forget to check out the video and practice problems below. Happy calculating! 🙂

## What are **Similar Triangles**?

When two triangles have congruent angles and proportionate sides, they are **similar**. This means they can be different in size (smaller or larger) but as long as they have the same angles and the sides are in proportion, they are similar! We use the “~” to denote similarity.

In the **Example** below, triangle ABC is similar to triangle DEF:

**How can we Prove Triangles Similar?**

There are three ways to prove similarity between two triangles, let’s take a look at each method below:

**Angle-Angle** **(AA): **When two different sized triangles have ** two angles that are congruent**, the triangles are similar. Notice in the example below, if we have the value of two angles in a triangle, we can always find the third missing value which will also be equal.

**Side-Side-Side (SSS): **When two different sized triangles have ** three corresponding sides in proportion **to each other, the triangles are similar.

**Side-Angle- Aside (SAS): **When two different sized triangles have ** two corresponding sides in proportion **to each other and a

**between each proportional side, the triangles are similar.**

*pair of congruent angles*Let’s look at how to apply the above rules with the following **Example:**

**Step 1: **Since, we know the triangles ABC and DEF are similar, we know that their corresponding sides must be in proportion! Therefore, we can set up a proportion and find the missing value of length EF by cross multiplying and solving for x.

**Practice Questions:**

1) Are the following triangles similar? If so, how? Explain.

2) Are the following triangles similar? If so, how? Explain.

3) Given triangle ABC is similar to triangle DEF, find the side of missing length AB.

4) Given triangle ABC is similar to triangle PQR, find the side of missing length AC.

## Solutions:

Still got questions? No problem! Don’t hesitate to comment with any questions below. Thanks for stopping by and happy calculating! 🙂

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