Unit 4 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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula is a² + b² = c², where c is the length of the hypotenuse.

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 6² + 8² = c²; 36 + 64 = c²; 100 = c²; c = 10.

Front

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

Back

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

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 a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; 169 = c²; c = 13.

Front

What is the length of the missing side if the hypotenuse is 13 and one side is 5?

Back

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

Front

What is an example of a real-world application of the Pythagorean Theorem?

Back

Determining the distance between two points on a map, or finding the height of a tree using its shadow.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

It is fundamental for understanding the properties of right triangles and is widely used in various fields such as architecture, engineering, and physics.