Prove the converse of the Pythagorean theorem using similar triangles. The converse of the Pythagorean theorem states that when

Question

3 years ago

8

Prove the converse of the Pythagorean theorem using similar triangles. The converse of the Pythagorean theorem states that when

the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. HELPPP

Mathematics

2 answers:

liraira [26] · Answer 1 · 2022-03-05T17:35:24+03:00

Answer:

Step-by-step explanation:By AA similarity postulate

△ADB∼△ABC∼△BDC

therefore the sides of the triangles are proportional, in particular

ADAB=ABAC ACBC=BCDC

By algebra we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

this is the same as

AD⋅AC=AB2AC⋅DC=BC2

"Equals added to equals are equal" allows us to add the equations

AD⋅AC+AC⋅DC=AB2+BC2

By distributive property

AC(AD+DC)=AB2+BC2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB2+BC2

this is equivalent to

AB2+BC2=AC2

which is what we wanted to prove

Whitepunk [10] · Answer 2 · 2022-03-05T15:54:05+03:00

Whitepunk [10]3 years ago

5 0

Answer:

I don't how to exactly put the explanation in words I hope this helps you

Step-by-step explanation: