Question Video: Determining the Similarity of Two Triangles | Nagwa Question Video: Determining the Similarity of Two Triangles | Nagwa

# Question Video: Determining the Similarity of Two Triangles Mathematics • Second Year of Preparatory School

## Join Nagwa Classes

The figure shows two triangles. Are the two triangles similar? Why?

01:48

### Video Transcript

The figure shows two triangles. Are the two triangles similar? Why?

In this question, we’re asked if these two triangles are similar. We can recall that similar triangles have corresponding angles congruent and corresponding sides in proportion. So, let’s have a look at the angles in both of these triangles. There’s a right angle of 90 degrees in each triangle. And one triangle has a 60-degree angle, and the other one has a 30-degree angle. However, if we remember that the angles in a triangle add up to 180 degrees, then we could calculate the third angle in each triangle.

In the top triangle, 60 plus the right angle of 90 degrees would give us 150 degrees, and subtracting that from 180 degrees would leave us with 30 degrees. In the lower triangle, 90 degrees plus 30 gives us 120 degrees, leaving us with a third angle of 60 degrees. What we can see then is that we have three pairs of equal angles. We have two 30-degree angles, two 60-degree angles, and two 90-degree angles. We have shown a three pairs of corresponding angles congruent. But in fact, we only need to show two pairs of corresponding angles congruent in order to show that two triangles are similar.

So, to answer the question “are the two triangles similar?” is yes. To answer the second question “why?,” we could say that if you calculate the measure of the third angle in one of the triangles, you can see that the triangles share two angles. Therefore, by the AA criteria, the triangles are similar.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions