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Given: triangle ABC is a right triangle, altitude CD

Prove: triangle CBD ~ triangle ACD

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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I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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