Ontario Mathematics Proficiency Practice Test

The triangle with sides measuring 8 cm, 6 cm, and 10 cm can be classified as a right triangle by applying the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we identify the sides as follows: 10 cm is the longest side, which we will consider as the hypotenuse. To verify if this triangle is a right triangle, we calculate:

1. Square the lengths of the three sides:

- Hypotenuse: 10 cm → \(10^2 = 100\)

- Other sides: 8 cm → \(8^2 = 64\) and 6 cm → \(6^2 = 36\)

2. Sum the squares of the two shorter sides:

- \(64 + 36 = 100\)

Since the sum of the squares of the two shorter sides equals the square of the hypotenuse (100 = 100), it confirms that the triangle adheres to the Pythagorean theorem. Thus, it is indeed a right triangle.