Pythagorean Theorem and 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 are the special right triangles?

Back

The special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the sides are in the ratio 1:1:√2. In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse (c), use the Pythagorean Theorem: c = √(a² + b²), where a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides 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 side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

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

Tags

CCSS.8.G.B.8

Front

What is an acute triangle?

Back

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

Tags

CCSS.4.G.A.2

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.2

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle measuring more than 90 degrees.

Tags

CCSS.4.G.A.2

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths (Pythagorean Theorem).

Tags

CCSS.8.G.B.8

Front

What is the formula for finding the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

Tags

CCSS.6.G.A.1