Similar Triangles: Analyzing the Relationship Between Triangle EDB and ABC

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

The order matters in the similarity statement! EDB ~ ABC means the first letter corresponds: E↔A, then D↔B, then B↔C. Always match vertices in the same position.

Q: Why are there so many different ratio expressions in the answer choices?

Each choice represents different vertex pairings. Only one pairing correctly matches the similarity statement EDB ~ ABC. The others mix up corresponding sides incorrectly.

Q: Can I write the ratios in a different order?

Yes! You can rearrange the equal ratios like $ \frac{AB}{BE} = \frac{BC}{DB} = \frac{AC}{ED} $, but the individual ratios must maintain correct corresponding sides.

Q: What if the triangles look different in size or position?

Similar triangles can be different sizes and orientations! Focus on the vertex labels and similarity statement, not how they appear visually in the diagram.

Q: How can I verify my answer is correct?

Check that each ratio uses corresponding sides from the correct triangles. For EDB ~ ABC: sides from triangle EDB go in numerator/denominator with sides from triangle ABC in the same positions.

Similar Triangles with Proportional Side Ratios

Triangle EDB is similar to triangle ABC.

Choose the correct answer.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate answer

00:03 The triangles are similar according to the given

00:08 According to the similarity ratio, we have pairs of corresponding sides

00:11 We'll go from each point to the next point to find the side

00:27 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

Triangle EDB is similar to triangle ABC.

Choose the correct answer.

Step-by-step solution

The key property of similar triangles is that the ratios of the lengths of their corresponding sides are equal. For triangles EDB and ABC:

Triangle EDB is similar to triangle ABC, meaning:
Corresponding sides are proportional: $\frac{AB}{BE} = \frac{BC}{DB} = \frac{AC}{ED}$

Therefore, the correct relationship among the sides, using the concept of similar triangles, is:

$\frac{BC}{DB} = \frac{AB}{BE} = \frac{AC}{ED}$

This matches choice 3.

Thus, the correct answer to the problem is $\frac{BC}{DB}=\frac{AB}{BE}=\frac{AC}{ED}$ .

Final Answer

$\frac{BC}{DB}=\frac{AB}{BE}=\frac{AC}{ED}$

Key Points to Remember

Essential concepts to master this topic

Similar Triangles: Corresponding sides are proportional with equal ratios
Matching Vertices: EDB ~ ABC means E↔A, D↔B, B↔C
Check Ratios: All three ratios must be equal: $\frac{BC}{DB} = \frac{AB}{BE} = \frac{AC}{ED}$ ✓

Common Mistakes

Avoid these frequent errors

Incorrect vertex correspondence in similar triangles
Don't randomly match vertices like E↔B or D↔A = wrong proportions! This leads to incorrect ratios that don't represent the true similarity relationship. Always match corresponding vertices based on the similarity statement order: EDB ~ ABC means E↔A, D↔B, B↔C.

Practice Quiz

Test your knowledge with interactive questions

If it is known that both triangles are equilateral, are they therefore similar?

FAQ

Everything you need to know about this question

How do I know which vertices correspond to each other?

The order matters in the similarity statement! EDB ~ ABC means the first letter corresponds: E↔A, then D↔B, then B↔C. Always match vertices in the same position.

Why are there so many different ratio expressions in the answer choices?

Each choice represents different vertex pairings. Only one pairing correctly matches the similarity statement EDB ~ ABC. The others mix up corresponding sides incorrectly.

Can I write the ratios in a different order?

Yes! You can rearrange the equal ratios like $\frac{AB}{BE} = \frac{BC}{DB} = \frac{AC}{ED}$ , but the individual ratios must maintain correct corresponding sides.

What if the triangles look different in size or position?

Similar triangles can be different sizes and orientations! Focus on the vertex labels and similarity statement, not how they appear visually in the diagram.

How can I verify my answer is correct?

Check that each ratio uses corresponding sides from the correct triangles. For EDB ~ ABC: sides from triangle EDB go in numerator/denominator with sides from triangle ABC in the same positions.

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