Pythagorean Theorem 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 can be expressed as: c² = a² + b².

Front

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

Back

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

Front

What is the length of the missing side if one side is 6 in and the hypotenuse is 10 in?

Back

8 in (Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).

Front

In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

What is the distance between two points (0,0) and (3,4) in a coordinate plane?

Back

5 units (Using the distance formula: √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5).

Front

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

Back

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

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 area of a right triangle with a base of 8 cm and a height of 6 cm?

Back

24 cm² (Area = 1/2 * base * height = 1/2 * 8 * 6).

Front

If a rectangle has a width of 5 m and a length of 12 m, what is the length of the diagonal?

Back

13 m (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The formula is: d = √(length² + width²), where d is the diagonal.