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The given triangle is a right triangle with an altitude to the hypotenuse.
â–³ ABC ~ â–³ ABD ~ â–³ BCD
We want to write a similarity statement relating the three triangles in the given diagram. To do so we can use the Right Triangle Altitude Theorem.
As we can see, △ ABC is a right triangle, ∠ABC is a right angle, and BD is the altitude to the hypotenuse. Having verified the necessary conditions, we can write the similarity statement. △ ABC ~ △ ABD △ ABC ~ △ BCD △ ABD ~ △ BCD
