A triangle has sides a , b , and c . Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=3 , b=4 , and c=5 .
Option A: Yes, a right triangle can be formed.
Option B: No, a right triangle cannot be formed.
Choose 1 for Option A or 2 for Option B.
(1 point)
1
Option A: Yes, a right triangle can be formed.
The Converse of the Pythagorean Theorem states that if the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, we can check if the triangle with sides a = 3, b = 4, and c = 5 satisfies this condition:
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
The equation holds true. Therefore, a triangle with these side lengths will indeed form a right triangle.
Hence, the correct answer is Option A.