Pythagorean Theorem and Right Triangles

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: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one leg of a right triangle is 9 and the other leg is 12, what is the length of the hypotenuse?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

In a triangle with sides 4, 8, and 10, is it obtuse, acute, or right?

Back

The triangle is obtuse.

Front

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

Back

In a right triangle, the square of the hypotenuse is greater than the square of each leg.

Front

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Back

It is a right triangle because 5² + 12² = 13².

Front

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

Back

Use the Pythagorean Theorem: c² = a² + b².

Front

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

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

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.