Question

Kurt wants to informally prove the converse of the Pythagorean Theorem by producing some evidence that supports it.

Recall that the converse of the Pythagorean Theorem states:

If a triangle has side lengths a,b,c, such that LaTeX: a^2+b^2\:=\:c^2a 2 + b 2 = c 2 , then the triangle is a right triangle. Kurt is going to construct several triangles with different side lengths. Select the TWO sets of three side lengths below that Kurt can use as evidence to support the converse of the Pythagorean Theorem.

Group of answer choices

20,48,52

4,5,6

7,24,25

9,12,16

Answer 1

Clearly if the three sides given form a right-angled triangle, then the largest side would be the hypotenuse.
So simply test if the sum of the squares of the two smaller sides equal the square of the largest.
e.g. 7,24,25
IS 7^ + 24^2 = 25^2 ??
49 + 576 = 625 ?
625 = 625 ? YES! So 7,24,25 form a right-angled triangle

test the others the same way