Pythagorean Theorem(find the missing side length)

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

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side. If a² + b² = c², then it is a right triangle.

Front

If a triangle has sides of lengths 60 yards, 63 yards, and 87 yards, is it a right triangle?

Back

Yes, because 60² + 63² = 3600 + 3969 = 7569, and 87² = 7569.

Front

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

Back

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

Front

What is the length of the missing side if one side is 8 and the other side is 15?

Back

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

Front

What is the hypotenuse of a right triangle with sides of lengths 9 and 12?

Back

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

Front

If a triangle has sides of lengths 7 kilometers, 10 kilometers, and 13 kilometers, is it a right triangle?

Back

No, because 7² + 10² = 49 + 100 = 149, and 13² = 169, which are not equal.

Front

What is the formula to find the length of a 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

What is the missing side if the hypotenuse is 25 and one side is 20?

Back

Using the Pythagorean Theorem: 20² + b² = 25²; 400 + b² = 625; b² = 225; b = 15.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it means that it is not a right triangle.