Pythagorean Theorem STAAR Review

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 is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.7

Front

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

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. If you know the lengths of two sides, you can rearrange the formula a² + b² = c² to solve for the missing side.

Tags

CCSS.8.G.B.7

Front

What is the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides. The formula is: Area = side².

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Front

If the area of a square is 25 in², what is the length of one side?

Back

To find the length of one side of a square with an area of 25 in², take the square root of the area: side = √25 = 5 in.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Front

What is the relationship between the areas of squares constructed on the sides of a right triangle?

Back

The areas of the squares constructed on the two shorter sides of a right triangle add up to the area of the square constructed on the hypotenuse. This is a direct consequence of the Pythagorean Theorem.

Tags

CCSS.8.G.B.8

Front

How do you calculate the diagonal length of a rectangle?

Back

The diagonal length (d) of a rectangle can be calculated using the Pythagorean Theorem: d = √(length² + width²).

Tags

CCSS.8.G.B.7

Front

What is the length of the diagonal of a piece of paper that is 11 inches tall and 8.5 inches wide?

Back

Using the formula for the diagonal of a rectangle: d = √(11² + 8.5²) = √(121 + 72.25) = √193.25 ≈ 13.9 in.

Tags

CCSS.8.G.B.8

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to determine distances and relationships between different points.

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. The side opposite the right angle is called the hypotenuse.