Question

How to finish my proof?

Answer 1

Ok, actually there's no picture. So, I was proving the Pythagorean Theorem and I was proving it using an altitude and similar triangles, but I realized I needed to write a proportion, but I don't know the reasoning to write a proportion of similar triangles?

Answer 2

Corresponding Parts of Congruent Triangles are Congruent

Answer 3

http://www.mathwarehouse.com/geometry/congruent_triangles/congruent-parts-CPCTC.php

Answer 4

@kliedako
How does that let you write a proportion?

Answer 5

read the link, understand it, digest the information, and then work on it. ^_^

Answer 6

Ok, I guess...
But CPCTC only works with Congruent triangles?

Answer 7

A `proportion` is simply setting two ratios equal to each other :
\[\dfrac{a}{b} = \dfrac{c}{d}\]

Answer 8

Yup, but since it's in my proof, I have to use a theorem to say why I did that, but I can't think of anything that fits. :(

Answer 9

When two triangles are similar, the corresponding sides form a proportion.
suppose \(\triangle ABC \sim \color{red}{\triangle DEF}\) then we have :
\[\dfrac{AB}{\color{red}{DE}} = \dfrac{BC}{\color{red}{EF}}\]

Answer 10

I think you may use AA similarity postulate to justify the similarity. It says two triangles are similar if two angle pairs are equal in both the triangles

Answer 11

Ok. I'll try...

Answer 12

@neonumbrella1234
There are a lot of ways you could do that, but I don't know if you need a theorem. Remember in class when he drew the two congruent triangles?

Answer 13

Sorry the three congruent triangles