Triangle Side Correspondence: Finding AB When Angles B=D and A=F

Q: How do I know which vertices correspond to each other?

Match the equal angles first! Since angle A = angle F and angle B = angle D, we know A corresponds to F and B corresponds to D. The remaining vertex C must correspond to E.

Q: Why does AB correspond to FD and not DF?

Side notation shows the order of vertices. Since A corresponds to F and B corresponds to D, side AB corresponds to side FD (F first, then D). The order matters!

Q: What if I can't see the angle markings clearly?

Look for the colored angle markers in the diagram. Equal angles will have the same color and shape markings. You can also use the given information that tells you which angles are equal.

Q: Do I need to prove the triangles are congruent?

No! The question asks for correspondence, not congruence. With two pairs of equal angles, we know the triangles are similar, which is enough to establish corresponding sides.

Triangle Correspondence with Angle-Angle Similarity

Look at the following two triangles:

Angles B and D are equal.
Angles A and F are equal.

Which side corresponds to AB?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Which side corresponds to side AB?

00:03 Angles are equal according to the given data

00:10 We can conclude that these angles are also equal

00:17 Let's write the similarity ratio according to the corresponding angles

00:29 We'll determine from the similarity ratio which side corresponds to AB

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following two triangles:

Angles B and D are equal.
Angles A and F are equal.

Which side corresponds to AB?

Step-by-step solution

As we have two equal angles, we will use the angle-angle theorem to simulate triangles.

We will compare the vertices: $A=F,B=D$

According to the data it seems that:

Side AC corresponds to side EF.

Side BC corresponds to side DE.

Therefore, side AB corresponds to side FD.

Final Answer

$FD$

Key Points to Remember

Essential concepts to master this topic

Angle-Angle Rule: Two equal angles prove triangles are similar
Vertex Matching: Match equal angles: A = F, B = D
Side Order: Corresponding sides follow vertex order precisely ✓

Common Mistakes

Avoid these frequent errors

Matching sides without considering vertex order
Don't randomly match sides like AB to any side in the second triangle = wrong correspondence! This ignores the critical vertex ordering established by equal angles. Always match vertices first (A=F, B=D), then determine corresponding sides based on that exact order.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know which vertices correspond to each other?

Match the equal angles first! Since angle A = angle F and angle B = angle D, we know A corresponds to F and B corresponds to D. The remaining vertex C must correspond to E.

Why does AB correspond to FD and not DF?

Side notation shows the order of vertices. Since A corresponds to F and B corresponds to D, side AB corresponds to side FD (F first, then D). The order matters!

What if I can't see the angle markings clearly?

Look for the colored angle markers in the diagram. Equal angles will have the same color and shape markings. You can also use the given information that tells you which angles are equal.

How can I check if my correspondence is correct?

List all three corresponding pairs:

A ↔ F (given: angles equal)
B ↔ D (given: angles equal)
C ↔ E (remaining vertices)

Then match sides: AB ↔ FD, BC ↔ DE, AC ↔ FE

Do I need to prove the triangles are congruent?

No! The question asks for correspondence, not congruence. With two pairs of equal angles, we know the triangles are similar, which is enough to establish corresponding sides.

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