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
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.
To determine whether a right triangle can be formed using the values of a, b, and c, we can use the Converse of the Pythagorean Theorem.
The Converse of the Pythagorean Theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Let's square the values of a, b, and c:
a^2 = 3^2 = 9
b^2 = 4^2 = 16
c^2 = ?
To check if a right triangle can be formed, we need to see if the sum of the squares of the two smaller sides (a^2 + b^2) is equal to the square of the longest side (c^2).
a^2 + b^2 = 9 + 16 = 25
Since a^2 + b^2 = c^2, we have:
25 = c^2
Therefore, a right triangle can be formed with the given values.
The answer is Option A: Yes, a right triangle can be formed.