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 form a right triangle?

Back

To determine if three sides 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 a, b, and c are the sides, then check if c² = a² + b².

Front

Given sides 15 cm, 8 cm, and 17 cm, do they form a right triangle?

Back

Yes, because 15² + 8² = 17² (225 + 64 = 289).

Front

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

Back

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

Front

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

Back

If you know two sides, you can find the missing side using the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) for one leg.

Front

Find the missing side if one side is 8 cm and the hypotenuse is 10 cm.

Back

The missing side is 6 cm, calculated as follows: 10² = 8² + b², so 100 = 64 + b², thus b² = 36, and b = 6.

Front

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

Back

In a right triangle, the hypotenuse is always the longest side, and the other two sides are called legs.

Front

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

Back

The other leg is 12, calculated as follows: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = 12.

Front

What does it mean if the Pythagorean Theorem holds true for a set of three sides?

Back

It means that the three sides can form a right triangle.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.