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Use the drop-down menus to complete the proof of the Pythagorean theorem.?

Use the drop-down menus to complete the proof of the Pythagorean theorem.

By the Choose( Side-Angle-Side Similarity Postulate, Angle-Angle Similarity Postulate, Side-Side-Side Similarity Postulate) , △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have Choose( Congruent, Proportional) sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a² = Choose( cd, cf, bc)and b2=ce . Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using the segment addition postulate gives a2+b2=c(c), which simplifies to a2+b2=c2 .
From choose pick one to complete with correct choices.

1 Answer
Feb 12, 2018


see below


angle-angle-angle similarity postulate

all angles being equal is what proves similarity. side-angle-side and side-side-side prove congruence. there is no indication that the two triangles in the picture are congruent; only similar.


similar triangles have angles that are all equal, and their sides are in the same ratios, but they are not necessarily congruent.


it is stated that #a^2+b^2 = cf + ce#. therefore #a^2 = cf#.