Mathematics

Marissa Vaughan

4 March, 08:08

Triangle ABC is a night triangle with CD I AB Angle C is a right angle

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

By the 1 Angie-Angie Similarity Postulate A ACB~AADC and A ACB~ACDB.

Since similar triangles have 2 proportional sides,

B B C and PE = AD Using cross

multiplication gives the equations (BC) ² = (BD) (BA) and (AC) ² = (AD) (AB). Adding these

together gives (BC) 2 + (AC) } = (BD) (BA) + (AD) (AB). Factoring out the common segment

gives (BC) ? + (AC) 2 = (AB) (BD + AD). Using 3 segment addition postulate gives

(BC) 2 + (AC) } = (AB) (AB), which simplifies to (BC) 2 + (AC) 2 = (AB) 2