Pythagorean Theorem - basics

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

What is the length of the hypotenuse if one side is 3 and the other side is 4?

Back

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

Front

How do you calculate the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

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

What is the length of the missing side if one side is 8 and the hypotenuse is 10?

Back

6 (Using the Pythagorean Theorem: 8² + b² = 10²; 64 + b² = 100; b² = 36; b = 6).

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

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 = 169).

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

What is the value of 5²?

Back

25.

Front

If one side of a right triangle is 9 and the hypotenuse is 15, what is the length of the other side?

Back

12 (Using the Pythagorean Theorem: 9² + b² = 15²; 81 + b² = 225; b² = 144; b = 12).