Look at the figure below: triangle abc has measure of angle abc equal to 90 degrees. e is a point on the hypotenuse ac such that the segment be is perpendicular to ac. d is a point outside the triangle on the right of e so that triangle edc has the measure of angle edc equal to 90 degrees. which triangle is similar to triangle aeb?

δaeb δabc δ bec

step-by-step explanation:

given:   ∠abc= , => ∠aeb =   , and ∠edc =  

let ∠bac = x , then by angle sum property in δabc, ∠bca = 90°-x

now, we can see, in δaeb, ∠bae = x (∵∠bac = x)

so, again by angle sum property in δaeb , ∠abe = 180°-x - 90° = 90°-x

in δabc & δaeb

∠abc=∠aeb (∵each 90°)

∠bac = ∠bae (∵ each equals to x)

∠acb = ∠abe = 90°-x

so, by aaa criteria of similarity

δaeb is similar to δabc

by using transitive property,

δaeb δabc δ bec

here, neither δedc nor δcde is similar to δaeb, beause ∠edc and ∠cde are arbitrary.

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step-by-step explanation: