Pythagoras

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 units and the other side is 4 units, what is the length of the hypotenuse?

Back

5 units (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What is the length of the hypotenuse if the two other sides are 5 m and 12 m?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

If the hypotenuse is 10 units and one side is 6 units, how do you find the other side?

Back

Use the Pythagorean Theorem: a² + 6² = 10². Therefore, a² + 36 = 100, so a² = 64, and a = 8 units.

Front

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

Back

Area = (1/2) * base * height.

Front

If a right triangle has an area of 24 square units and a base of 8 units, what is the height?

Back

6 units (Using the area formula: 24 = (1/2) * 8 * height, so height = 6).

Front

What is a right triangle?

Back

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

Front

What is the definition of a hypotenuse?

Back

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

Front

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

Back

It is an isosceles right triangle.