8.MG.4

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 does the converse of the Pythagorean Theorem state?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides using the Pythagorean Theorem.

Front

What is a right triangle?

Back

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

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

What is the hypotenuse of a right triangle?

Back

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

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, it is a right triangle because 8² + 15² = 17² (64 + 225 = 289).

Front

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

Back

Yes, it is a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

What is the relationship between the legs and the hypotenuse of a right triangle?

Back

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse (a² + b² = c²).

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).