Triangle Similarity Problem: Comparing Angles of 70° and 35°

Angle B is equal to 70 degrees

Angle C is equal to 35 degrees

Angle E is equal to 70 degrees

Angle F is equal to 35 degrees

Are the triangles similar?

AAABBBCCCDDDEEEFFF

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are the triangles similar?
00:03 The sum of angles in a triangle equals 180
00:10 Let's substitute appropriate values and solve for angle A
00:17 This is the size of angle A
00:22 Let's use the same method in the second triangle
00:29 Let's substitute appropriate values and solve for angle D
00:36 This is the size of angle D
00:39 All angles are equal between the triangles, therefore they are similar by AA similarity
00:44 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Angle B is equal to 70 degrees

Angle C is equal to 35 degrees

Angle E is equal to 70 degrees

Angle F is equal to 35 degrees

Are the triangles similar?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

The triangles are similar according to the angle-angle theorem.

Having two pairs of equal angles is sufficient to conclude that the triangles are similar.

3

Final Answer

Yes

Practice Quiz

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Is the similarity ratio between the three triangles equal to one?

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