Pythagorean Theorem/Special 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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY applies to right triangles.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 45-45-90 triangle in relation to each other?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 4?

Back

The hypotenuse is 4√2.

Tags

CCSS.8.G.B.7

Front

Can the lengths 4 cm, 7 cm, and 2 cm form a triangle?

Back

No, these lengths cannot form a triangle because they do not satisfy the triangle inequality theorem.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

What is the length of the hypotenuse in a right triangle with legs of length 5 and 5?

Back

The hypotenuse is 5√2.

Tags

CCSS.8.G.B.7

Front

What is a special right triangle?

Back

Special right triangles are triangles with specific angle measures (like 45-45-90 and 30-60-90) that have predictable side length ratios.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 30-60-90 triangle in relation to each other?

Back

In a 30-60-90 triangle, the length of the side opposite the 30° angle is half the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse in a 30-60-90 triangle with a shorter leg of length 6?

Back

The hypotenuse is 12.

Tags

CCSS.8.G.B.8