Question

How do you show that a triangle with vertices `(13,-2)`, `(9,-8)`, `(5,-2)` is isosceles?

Answer 1

Find the length of the triangle's segments and prove that two are equal but the third is different. In case, `P1P1=P2P3=sqrt(50)` and `P1P3=8` => `triangle_(P1P2P3)` is isosceles

Explanation:

Length of the triangle's segments:
`P1P2=sqrt((9-13)^2+(-8+2)^2)=sqrt (16+36)=sqrt(50)`
`P1P3=sqrt((5-13^2+(-2+2)^2)=sqrt(64+0)=8`
`P2P3=sqrt((5-9)^2+(-2+8)^2)=sqrt(16+36)=sqrt(50`

As we can see two sides of the triangle are equal (`P1P2=P2P3=sqrt(50)`) but the third one is different (`P1P3=8`): so `triangle_(P1P2P3)` is isosceles.