Question

The vertices of triangle DEF are D(7, 3), E(4, -3), and F(10, -3). Write a paragraph proof to prove that triangle DEF is isosceles.

Answer 1

Proof method: 

1. Calculate the length of each side, DE,DF,EF

2. Compare the length of them, if any pair of them is equal, then it's isosceles.

Answer 2

I am given that the vertices of triangle DEF are D(7, 3), E(4, -3), and F(10, -3). Applying the distance formula to each pair of vertices in the triangle gives the following:

Two of the sides, DE and DF, have the same length. So, by definition of an isosceles triangle, triangle DEF is isosceles.