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Question
Given: triangle ABC is a right triangle, altitude CD
Prove: triangle CBD ~ triangle ACD

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Questioner:Athena Apodaca  
Country:Arizona, United States
Category:Advanced Math
Private:No
Subject:Proofs. Right triangle altitude

Question:
Given: triangle ABC is a right triangle, altitude CD
Prove: triangle CBD ~ triangle ACD
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On the assumption that angle C is the right angle: (Not stated -- you should)

You have triangles CBD and ACD.  (You did well to name them correctly, with corresponding vertices in the same spots.)

1. Identify a relation between angle CAD and angle ACD.
2. Identify a relation between angle DCB and angle ACD.
3. Use those to deduce a relation between angle CAD and angle BCD. (Guess what you are going to prove about them)

Now find another pair of corresponding angles in your triangles and prove they are equal.

Take it from there.
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NOTE:  Advanced Math is precalculus and trigonometry.  Send these to the Geometry section.

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