Question

D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF?

Answer 1

DE^2 = 1 + 16 = 17.

EF^2 = 16 + 1 = 17.

DF^2 = 9 + 25 = 34.

Since (DE)^2 + (EF)^2 = (DF)^2,

angle E is 90 degrees.

DF must be the hypotenuse

Here look at that

Answer 2

m∠DEF is 90°

Explanation:

It is given that D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. Thus, using the distance formula, we have

⇒

⇒

and

⇒

⇒

Also,

⇒

⇒

Now,

⇒

⇒

Thus, Pythagoras theorem holds.

Hence, m∠DEF is 90°⇒ΔDEF is right angled triangle which is right angled at E.