Question

Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths of 2 cm, 3 cm, 4 cm, and 5 cm.

A. Show that the square of the longest side is equal to the sum of the squares of the other two sides.
B. Show that the sum of the squares of the two shorter sides is equal to the square of the longest side.
C. Show that the product of the two shorter sides is equal to half the product of the longest side and the middle side.

Answer 1

Option B, which states that the sum of the squares of the two shorter sides is equal to the square of the longest side, can be used to show the converse of the Pythagorean theorem using side lengths of 2 cm, 3 cm, 4 cm, and 5 cm.

Step-by-step explanation:

The procedure that can be used to show the converse of the Pythagorean theorem using side lengths of 2 cm, 3 cm, 4 cm, and 5 cm is option B.

The converse of the Pythagorean theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.

In this case, if we show that 2² + 3² = 13 and 4² = 5² = 25, we can see that the sum of the squares of the two shorter sides (13) is equal to the square of the longest side (25), which confirms the converse of the Pythagorean theorem.