Question

GEOMETRY HELP PLEASE I AM DESPERATE

Answer 1

what's your question?

Answer 2

Prove the Converse of the Pythagorean Theorem. The converse of the Pythagorean thearom states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle.

Answer 3

hello please help

Answer 4

ok let me think

Answer 5

ok

Answer 6

ok have a look at this PDF

specifically, look on page 2

http://www.charleston.k12.il.us/cms/Teachers/math/PreAlgebra/paunit8/L8-1.PDF

tell me what you think and if it helps you at all. If not, then we can try another way

Answer 7

It didnt really help me

Answer 8

ok we start off with a^2 + b^2 = c^2

we're given this

Answer 9

we want to prove that if that is true, then the triangle has to be a right triangle

Answer 10

so say we have this triangle

Answer 11

let's also say we had another right triangle with legs a and b

the right triangle will have a hypotenuse of n

Answer 12

by the pythagorean theorem, we can say

a^2 + b^2 = n^2

Answer 13

we're given a^2 + b^2 = c^2

we just found that a^2 + b^2 = n^2

those two left sides are the same, that means c^2 = n^2

take the square root of both sides to get c = n

Answer 14

so that proves the triangle on the left *has* to be a right triangle for a^2 + b^2 = c^2 to be true

Answer 15

So like how do I put that into words since I cant use pictures

Answer 16

you'll just have to describe the pictures. So say something like "start with any general triangle with sides a,b,c." or "we'll have the right triangle with legs a & b with hypotenuse n"

Answer 17

ok then what

Answer 18

what do you have so far?

Answer 19

we'll have the right triangle with legs a & b with hypotenuse n"

Answer 20

then you can add on something like "by the pythagorean theorem, we can say that a^2 + b^2 = n^2"

Answer 21

also before all that, you should have statements that declare what you're given, which is: a^2 + b^2 = c^2

Answer 22

ok now what

Answer 23

then by substitution, we can say that because a^2 + b^2 = n^2 and a^2 + b^2 = c^2, we know that c^2 = n^2

Answer 24

then the square root property of equality then allows us to get to c = n

Answer 25

so effectively, a^2 + b^2 = c^2 is the exact same as a^2 + b^2 = n^2. Because the triangle with side n is a right triangle, that forces the triangle with a,b,c to also be a right triangle

Answer 26

thank you so much!

Answer 27

you're welcome