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). It is expressed as: a² + b² = c².

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: 3² + 4² = c² => 9 + 16 = c² => c² = 25 => c = 5).

Front

What are the side lengths of a right triangle if a = 5 and b = 12?

Back

c = 13 (Using the Pythagorean Theorem: 5² + 12² = c² => 25 + 144 = c² => c² = 169 => c = 13).

Front

Do the side lengths 8, 15, and 17 form a right triangle?

Back

Yes, they form a right triangle (8² + 15² = 17² => 64 + 225 = 289 => 289 = 289).

Front

Which of the following sets of lengths form a right triangle: 7, 24, 25?

Back

Yes, they form a right triangle (7² + 24² = 25² => 49 + 576 = 625 => 625 = 625).

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If b = 35 and c = 37, what is a?

Back

a = 12 (Using the Pythagorean Theorem: a² + 35² = 37² => a² + 1225 = 1369 => a² = 144 => a = 12).

Front

What is the value of c if a = 9 and b = 40?

Back

c = 41 (Using the Pythagorean Theorem: 9² + 40² = c² => 81 + 1600 = c² => c² = 1681 => c = 41).

Front

Do the lengths 12, 20, and 16 form a right triangle?

Back

Yes, they form a right triangle (12² + 16² = 20² => 144 + 256 = 400 => 400 = 400).

Front

Which set of lengths does not form a right triangle: 14, 15, 29?

Back

14, 15, 29 do not form a right triangle (14² + 15² ≠ 29² => 196 + 225 ≠ 841).