Pythagorean Theorem PRACTICE

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

How can you determine if three sides can form a right triangle?

Back

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

Front

Given sides 9 ft, 20 ft, and 14 ft, do they form a right triangle?

Back

No, because 9² + 14² = 81 + 196 = 277, which is not equal to 20² (400).

Front

Find the missing side if one side is 8 and the other is 15. What is the hypotenuse?

Back

Using the Pythagorean Theorem: 8² + 15² = c²; 64 + 225 = c²; 289 = c²; c = 17.

Front

What is the hypotenuse of a right triangle with legs of 12 in and 16 in?

Back

Using the Pythagorean Theorem: 12² + 16² = c²; 144 + 256 = c²; 400 = c²; c = 20 in.

Front

If a triangle has sides of 15 cm, 8 cm, and 17 cm, does it form a right triangle?

Back

Yes, because 15² + 8² = 225 + 64 = 289, which is equal to 17² (289).

Front

What is the formula to find the length of a side in a right triangle?

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If one leg of a right triangle is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12.

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 (legs) equals the square of the longest side (hypotenuse).

Front

Can a triangle with sides 7, 24, and 25 be a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, which is equal to 25² (625).