Question

Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures. (GEOMETRY)

Answer 1

check my work please

Answer 2

By Angle Angle Similarity Postulate

Triangle ADB is congruent to triangle ABC is congruent to triangle BDC

The side of the triangle are proportional ,
AD/AB = AB/AC
AC/BC = BC/DC

By cross multiplication we have the following equations:
AD * AC = AB * AB
AC * DC = BC * BC

Which is the same as:
AD * DC = BD^2
AD * AC = AB^2
AC * DC = BD^2

Add the two equations:
AD * AC AC * DC = AB^2 BC^2

By the distributive property:
AC(AD DC) = AB^2 BC^2

but by construction AD DC = AC...so we have:
AC * AC = AB^2 BC^2

Which is equivalent to:
AB^2 BC^2 = AC^2

Answer 3

@malcolmmcswain @just_one_last_goodbye @sleepyjess @superdavesuper

Answer 4

I think that's right. No mistakes I can see. I might have missed one, though.

Answer 5

You're missing some plus signs... is that just a typo?
Example:
"By the distributive property:
AC(AD DC) = AB^2 BC^2"
should be
"By the distributive property:
AC(AD + DC) = AB^2 + BC^2"

Answer 6

oopd , i didn't notice that . thank you.