Pythagorean Theorem

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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: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

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

Back

To find the length of a missing side, rearrange the Pythagorean Theorem formula. If you know the lengths of the other two sides, you can solve for the missing side by using: a = √(c² - b²) or b = √(c² - a²).

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CCSS.8.G.B.7

Front

What is a right triangle?

Back

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

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CCSS.4.G.A.2

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is a scale factor in geometry?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar shapes, it is the ratio of the lengths of corresponding sides.

Tags

CCSS.7.G.A.1

Front

If the scale factor from a small shape to a big shape is 2, what does this mean?

Back

It means that each side of the big shape is twice as long as the corresponding side of the small shape.

Tags

CCSS.7.G.A.1

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Tags

CCSS.HSG.SRT.A.2

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, where 1 is the length of the side opposite the 30-degree angle, √3 is the length of the side opposite the 60-degree angle, and 2 is the length of the hypotenuse.

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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 length of the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

How can you use the Pythagorean Theorem to solve for the hypotenuse?

Back

To solve for the hypotenuse (c), use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.8