Similar Triangles Investigation: Comparing Triangles ABC and DEF

Triangle Similarity with Angle-Angle Comparison

Are the below 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 Isosceles triangle according to the given
00:07 In an isosceles triangle, base angles are equal
00:11 Sum of angles in a triangle equals 180
00:15 Therefore the third angle equals 180 minus the known angles
00:20 Equal angles according to the given
00:26 Let's substitute the angle value
00:35 Isosceles triangle according to the given
00:39 In an isosceles triangle, base angles are equal
00:44 The angles sum to 180
00:48 Therefore each angle equals A
00:53 Equal angles (EA)
01:01 The triangles are similar by AA
01:11 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Are the below triangles similar?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

Use the similarity theorems.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • AA Similarity: Two triangles are similar if two angles are equal
  • Technique: Check if ∠A = ∠D and ∠B = ∠E from the diagram
  • Check: If two angles match, third angle automatically matches too ✓

Common Mistakes

Avoid these frequent errors
  • Only checking one angle for similarity
    Don't assume triangles are similar with just one matching angle = inconclusive result! One angle isn't enough because many different triangles can share the same angle. Always check at least two angles using AA similarity theorem.

Practice Quiz

Test your knowledge with interactive questions

Angle B is equal to 60°

Angle C is equal to 55°

Angle E is equal to 60°

Angle F is equal to 50°

Are these triangles similar?

AAABBBCCCDDDEEEFFF

FAQ

Everything you need to know about this question

Why don't I need to check all three angles?

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Great question! If two angles match, the third angle must also match because angles in any triangle always add up to 180°. This is why AA Similarity works!

What if the triangles look different sizes?

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Similar triangles can be different sizes! They just need the same shape (same angles). Think of a small photo and a large poster - same image, different sizes.

How can I identify corresponding angles?

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Look for angle markings in the diagram, or identify angles by their position. Corresponding angles are in the same relative position in each triangle.

Do I need to measure the sides too?

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No! For similarity, you only need to check angles using AA theorem. Side lengths would only matter if you were checking for congruence (exactly the same size and shape).

What if I can't see angle measurements?

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Look for angle markings (like small arcs or squares), parallel lines, or other geometric clues. Sometimes you need to use vertical angles or corresponding angles to find equal angles.

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