Pythagorean Theorem Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. If a² + b² = c² holds true, then it is a right triangle.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which equals 5².

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) of a rectangle can be found using the formula: d = √(length² + width²).

Front

Calculate the diagonal of a rectangle with a length of 120 m and a width of 90 m.

Back

d = √(120² + 90²) = √(14400 + 8100) = √22500 = 150 m.

Front

What are the properties of a right triangle?

Back

1. One angle is 90 degrees. 2. The side opposite the right angle is the longest side (hypotenuse). 3. The Pythagorean Theorem applies.

Front

Can a triangle with sides 4, 5, and 6 be a right triangle?

Back

No, because 4² + 5² = 16 + 25 = 41, which does not equal 6² (36).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a triangle has sides of lengths 41, 24, and 32, is it a right triangle?

Back

No, because 41² + 24² = 1681 + 576 = 2257, which does not equal 32² (1024).