Asked by Kenyell
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
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
Answers
Answered by
Reiny
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
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
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