In sondras math class the teacher gives all of the students the digram below where ab is perpendicular to bc and ac is perpendicular to bd. sondra works with her classmates to prove that triangle abc, triangle abd and triangle bdc are all similiar right triangles. based on the similarity of the three right triangles, show (AB) 2 + (BC) 2 = (AC) 2

Question

Annika Potter

Mathematics

30 December, 08:57

In sondras math class the teacher gives all of the students the digram below where ab is perpendicular to bc and ac is perpendicular to bd. sondra works with her classmates to prove that triangle abc, triangle abd and triangle bdc are all similiar right triangles. based on the similarity of the three right triangles, show (AB) 2 + (BC) 2 = (AC) 2

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Julissa Church · Answer 1

Given the set up of the diagram, AB^2 will equal AC x AD and BC^2 will equal AC x DC. To solve, substitute AB^2 + BC^2 with (AC x AD) + (AC x DC). Then, take out like terms through the distributive property: AC (AD + DC). AD + DC is equal to AC. So, AC x AC = AC^2.