Question

Right triangle ABC has altitude d. Move the options into the spaces to complete the proof of the Pythagorean Theorem. By angle-angle similarity, ? ABC ~ ? ACD ~ ? CBD and the proportions [ ] and [ ] are true. The two proportions can be cross-multiplied and added together to form the equation [ ]. This equation can be simplified to result in the Pythagorean Theorem, a^2 + b^2 = c^2. a/c = f/a; a/c = c/b; b/c = f/b; d/f = e/d ac + bc = ae + bf; a^2 + b^2 = ce + cf; a^2 + d^2 = ce + ef; b^2 + d^2 = cf + ef

          Right triangle ABC has altitude d.
Move the options into the spaces to complete the proof of the Pythagorean Theorem.
By angle-angle similarity, ? ABC ~ ? ACD ~ ? CBD and the proportions [ ] and [ ] are true. The two proportions can be cross-multiplied and added together to form the equation [ ]. This equation can be simplified to result in the Pythagorean Theorem, a^2 + b^2 = c^2.
a/c = f/a; a/c = c/b; b/c = f/b; d/f = e/d
ac + bc = ae + bf; a^2 + b^2 = ce + cf; a^2 + d^2 = ce + ef; b^2 + d^2 = cf + ef

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Right triangle ABC has altitude d.
Move the options into the spaces to complete the proof of the Pythagorean Theorem.
By angle-angle similarity, ? ABC ? ACD ? CBD and the proportions [ ] and [ ] are true. The two proportions can be cross-multiplied and added together to form the equation [ ]. This equation can be simplified to result in the Pythagorean Theorem, a^2 + b^2 = c^2.
a/c = f/a; a/c = c/b; b/c = f/b; d/f = e/d
ac + bc = ae + bf; a^2 + b^2 = ce + cf; a^2 + d^2 = ce + ef; b^2 + d^2 = cf + ef

Added by Dawn A.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

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Solved by Expert Jerelyn Nevil

05/17/2023

Step 1

We have a right triangle ABC with altitude d. The altitude divides the hypotenuse into two segments, CD and BD. We are given that by angle-angle similarity, triangle ABC is similar to triangles ACD and CBD. Show more…

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Right triangle ABC has altitude d. Move the options into the spaces to complete the proof of the Pythagorean Theorem: By angle-angle similarity, ABC ~ ACD ~ CBD and the proportions are true. The two proportions can be cross-multiplied and added together to form the equation This equation can be simplified to result in the Pythagorean Theorem, a^2 + b^2 = c^2 ac + bc = ae + bf a^2 + d^2 = ce + ef

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