Thank you for visiting In rectangle ABCD E is on DC such that AEB 90 Prove that triangles ADE AEB and EBC are similar. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
To prove that triangles ADE, AEB, and EBC are similar, we need to show that their corresponding angles are equal and their corresponding side lengths are proportional.
Explanation:
To prove that triangles ADE, AEB, and EBC are similar, we need to show that their corresponding angles are equal and their corresponding side lengths are proportional.
- First, we know that angle AEB = 90 degrees, as given in the question.
- We can also see that angle AED = angle AEB, because they are alternate interior angles formed by a transversal and a pair of parallel lines (AE and BC).
- Next, angle DEB = angle ABC, because they are vertical angles.
- Finally, we can find that angle EBC = angle EDA, because they are alternate interior angles formed by a transversal and a pair of parallel lines (AE and BC).
Since all corresponding angles are equal, we can conclude that triangles ADE, AEB, and EBC are similar.
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