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: c² = a² + b².

Front

Identify the hypotenuse in a right triangle.

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

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

Front

Which set of sides can form a right triangle? 5, 12, 13 or 4, 5, 6?

Back

5, 12, 13 can form a right triangle (5² + 12² = 25 + 144 = 169; √169 = 13).

Front

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

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has sides of length 6 and 8, what is the length of the hypotenuse?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100; √100 = 10).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.