In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.

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04-08-2022
Mathematics

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In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.

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Akposevictoridn Akposevictoridn · Answer 1 · 2022-08-05T13:59:30-04:00

Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

What is the Angle-angle Similarity Theorem (AA)?

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

Learn more about the angle-angle theorem (AA) on:

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What is the Angle-angle Similarity Theorem (AA)?

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