Question

Determine whether each of the following triangles is a right triangle. If it is, which angle is the right angle? Please explain your answer in a sentence and show your work.

(a) △ABC with a=10, b=24, c=26
(b) △DEF with d=13, e=85, f=84
(c) △GHI with g=40, h=10, i=41
(d) △PQR with p=18.5, q=6, r=17.5
(e) △STU with s=√11, t=7, u=√38
(f) △WXY with w=5, x=√40, y=8
√ is square root.

Answer 1

Use a² + b² = c², where "a" and "b" are the smallest two numbers, and "c" is the biggest number.

So testing each:
(a) Yes, a right triangle.
(b) Yes, a right triangle.
(c) Not a right triangle.
(d) Yes, a right triangle.
(e) Yes, a right triangle. (The two smallest sides are √11 and √38)
(f) Not a right triangle.