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: a² + b² = c².

Front

In a right triangle, if one leg is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

If the hypotenuse of a right triangle is 13 units and one leg is 5 units, how do you find the length of the other leg?

Back

Use the Pythagorean Theorem: a² + 5² = 13²; a² + 25 = 169; a² = 144; a = 12 units.

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. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.

Front

How do you calculate the distance between two points on a coordinate grid?

Back

Use the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Front

What is the area of a square with a side length of 12 units?

Back

Area = side² = 12² = 144 square units.

Front

If the area of square A is 100 ft², what is the length of one side?

Back

Length of one side = √Area = √100 = 10 ft.

Front

What is the formula for the area of a right triangle?

Back

Area = (1/2) × base × height.

Front

In a right triangle, if one leg is 8 units and the hypotenuse is 10 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 8² = 10²; a² + 64 = 100; a² = 36; a = 6 units.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to determine distances and relationships between points.