Pythagorean 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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula is a² + b² = c².

Front

A rectangular field is 30 yards wide and 40 yards long. How far is the diagonal across the field?

Back

50 yards (Using the Pythagorean Theorem: 30² + 40² = 900 + 1600 = 2500; √2500 = 50).

Front

What is the length of the missing side if one side is 12 in. and the hypotenuse is 13 in.?

Back

5 in. (Using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5).

Front

In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

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

Back

The sum of the squares of the two legs equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle (5² + 12² = 25 + 144 = 169 = 13²).

Front

What is the length of the hypotenuse if the legs are 8 cm and 15 cm?

Back

17 cm (Using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).