Finding Corresponding Angles: Triangle ABC vs Triangle DEF

Corresponding Angles with Triangle Similarity

Look at the two triangles below:

AAABBBCCCDDDEEEFFF

Angle B is equal to angle E.
Angle A is equal to angle D.

Which angle corresponds to angle C?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's find out what angle matches with angle C.
00:06 Angles are equal, as given in the data.
00:10 The triangles are similar by the angle-angle rule, or A.A.
00:15 So, the matching angle is the last angle, angle F.
00:20 And there you have it, that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the two triangles below:

AAABBBCCCDDDEEEFFF

Angle B is equal to angle E.
Angle A is equal to angle D.

Which angle corresponds to angle C?

2

Step-by-step solution

As we have two pairs of corresponding angles, we will use the angle-angle theorem for triangle similarity.

Now that we know all angles are equal to each other, we note that the remaining angle that is equal and corresponds to angle C is angle F.

3

Final Answer

F F

Key Points to Remember

Essential concepts to master this topic
  • Rule: Corresponding angles in similar triangles are equal
  • Technique: Use given pairs to identify pattern: B = E, A = D
  • Check: All angle pairs match triangle vertices in same order ✓

Common Mistakes

Avoid these frequent errors
  • Matching angles without considering vertex order
    Don't randomly match remaining angles like C = D or C = E = wrong correspondence! This ignores the systematic pattern of vertex matching. Always follow the established correspondence pattern from given angle pairs.

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

How do I know which angles correspond?

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Look at the given information first! If angle B = angle E and angle A = angle D, then the triangles match in order ABC ↔ DEF, so angle C must equal angle F.

What if the triangles look different sizes?

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Size doesn't matter for corresponding angles! Similar triangles have the same shape but different sizes, so all corresponding angles are equal regardless of triangle size.

Can I use any two equal angles to prove similarity?

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Yes! The Angle-Angle (AA) theorem says if two angles in one triangle equal two angles in another triangle, the triangles are similar and the third angles must also be equal.

What's the difference between similar and congruent triangles?

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Similar triangles have equal angles but different side lengths. Congruent triangles have both equal angles AND equal side lengths.

How do I remember the correspondence order?

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Write the triangles in the same order as the given equal angles: if B = E and A = D, then ABC corresponds to EDF... wait, that's wrong! Always keep vertex order: ABC ↔ DEF.

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