Question

Help!!
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 lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.

Answer 1

I can prove it using congruent triangles.

Answer 2

That's fine, what is it?

Answer 3

So what's the proof?

Answer 4

let ABC be a triangle where AB^2 = CB^2 + AC^2
WE say that angle ACB is right angled
Draw a line segment BCD so that BC = CD
Now join AD

Answer 5

Since DC = CB the square on BC must equal the square on DC . DC^2 = CB^2.
Now Add the square on AC to each then DA^2 + DC^2 = DA^2 + CB^2

Answer 6

Wait but if you're adding the square of AC then how do you get DA^2 + DC^2 = DA^2 + CB^2?

Answer 7

SOrry the last statement should read AC^2 + DC^2 = AC^2 + CB^2

Answer 8

But we are given that AB^2 = AC^2 + CB^2

and therefore AB^2 = AD^2

( I think you call that the transitive property of equality in the US)

Answer 9

so AD = AB

and we are given that DC=BC and AD = AD
therefore the 2 triangle are congruent by SSS

Answer 10

Ohh ok, thanks that helped a lot :)

Answer 11

Finally the 2 angles ACD = ACB so they both must be right angles
therefore triangle ABC is a right angle.

Answer 12

Yeah thanks I was mostly confused about one of the parts but you explained it great, thank you

Answer 13

yw

Answer 14

yeah I had a mental 'blip'.

Answer 15

- or at my age its called a 'senior moment' LOL

Answer 16

THis proof is due to Euclid .