Pythagorean Review Flashcardziz

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 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

How do 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.

Tags

CCSS.8.G.B.8

Front

What are the side lengths of a 5-12-13 triangle?

Back

The side lengths are 5, 12, and 13, which satisfy the Pythagorean theorem: 5² + 12² = 13².

Tags

CCSS.8.G.B.8

Front

If one leg of a right triangle is 12 and the other leg is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 13, calculated using the Pythagorean theorem: √(12² + 5²) = √(144 + 25) = √169 = 13.

Tags

CCSS.8.G.B.7

Front

What is the hypotenuse in a right triangle with legs of lengths 9 and 12?

Back

The hypotenuse is 15, calculated using the Pythagorean theorem: √(9² + 12²) = √(81 + 144) = √225 = 15.

Tags

CCSS.8.G.B.7

Front

Can the lengths 15, 12, and 9 form a right triangle?

Back

Yes, they can form a right triangle because 15² = 12² + 9².

Tags

CCSS.8.G.B.8

Front

What is the height of a tree if it casts a shadow of 4.2 meters and the angle of elevation is known?

Back

The height of the tree can be calculated using trigonometric ratios, but in this case, it is given as 4.2 meters.

Tags

CCSS.HSG.SRT.C.8

Front

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

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Tags

CCSS.6.G.A.1

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.

Tags

CCSS.HSG.CO.C.10