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). It can be expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : √3 : 2. The short leg is opposite the 30-degree angle, the long leg is opposite the 60-degree angle, and the hypotenuse is twice the length of the short leg.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

To find the length of the hypotenuse in a 30-60-90 triangle, multiply the length of the short leg by 2.

Tags

CCSS.8.G.B.8

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.2

Front

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

Back

In a right triangle, the lengths of the sides must satisfy the Pythagorean Theorem: a² + b² = c², where c is the length of the hypotenuse.

Tags

CCSS.8.G.B.8

Front

What is the long leg in a 30-60-90 triangle?

Back

The long leg in a 30-60-90 triangle is the side opposite the 60-degree angle, and its length is √3 times the length of the short leg.

Tags

CCSS.HSG.CO.C.10

Front

What type of triangle has angles measuring 90 degrees, 60 degrees, and 30 degrees?

Back

A 30-60-90 triangle.

Tags

CCSS.4.G.A.2

Front

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

Back

To determine if three lengths can form a right triangle, check if they satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Tags

CCSS.8.G.B.8

Front

What is the short leg in a 30-60-90 triangle?

Back

The short leg in a 30-60-90 triangle is the side opposite the 30-degree angle.

Tags

CCSS.HSG.CO.C.10

Front

What is the formula to find the area of a right triangle?

Back

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

Tags

CCSS.6.G.A.1