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

Question

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

+1

Answers (1)

Know the Answer?

Francis · Answer 1

Angle by angle similarity postulate.

Step-by-step explanation:

All angles being equal is what proves the side-angle-side and side-side-side congruence.

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

therefore, A² + B² = CF + CE

Therefore, A² = CF