8.GSR.8.2 Pythagorean Theorem

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

What is a hypotenuse?

Back

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

Front

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

Back

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

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 a right triangle has a hypotenuse of 10 cm and one leg of 6 cm, what is the length of the other leg?

Back

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

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

In a right triangle, if the legs are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

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

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If a ladder is 13 feet long and the base is 5 feet from the wall, how high does it reach?

Back

12 feet (using the Pythagorean Theorem: 13² = 5² + h²; 169 = 25 + h²; h² = 144; h = 12).

Front

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

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and relationships between different points.