Pythagorean 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

What is the hypotenuse in a right triangle?

Back

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

Front

If one side of a right triangle is 15 and the hypotenuse is 21, how do you find the missing side?

Back

Use the Pythagorean Theorem: a² + 15² = 21². Solve for a.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If the lengths of the two legs of a right triangle are 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225. Therefore, c = √225 = 15.

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

How do you determine if a triangle is a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem: a² + b² = c².

Front

What is the value of x if x² + 15² = 21²?

Back

x² + 225 = 441. Therefore, x² = 441 - 225 = 216, so x = √216 = 14.7.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

If a right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17.