Pythagorean Theorem and Special Right Triangle

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.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 45-45-90 triangle?

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 a leg.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

Multiply the length of one leg by √2.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is twice the length of the shortest side (the side opposite the 30° angle).

Tags

CCSS.8.G.B.8

Front

Does the set of numbers 20, 25, 15 represent a right triangle?

Back

Yes, because 20² + 15² = 400 + 225 = 625 = 25².

Tags

CCSS.8.G.B.8

Front

What is the condition for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).

Front

If a triangle has sides of lengths 15, 12, and 9, does it exist?

Back

Yes, because 15 < 12 + 9, 12 < 15 + 9, and 9 < 15 + 12.

Tags

CCSS.7.G.A.2

Front

What is the formula to check if a triangle is a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Tags

CCSS.8.G.B.8

Front

In a 30-60-90 triangle, what is the length of the longer leg if the shortest leg is 4?

Back

The longer leg is 4√3.

Tags

CCSS.8.G.B.8