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.

Front

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

Back

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

Front

If one side of a right triangle is 3 inches and the other side is 4 inches, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 inches.

Front

What is a right triangle?

Back

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

Front

Can the sides 8, 15, and 17 form a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, which is equal to 17².

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

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 Pythagorean Theorem holds true: a² + b² = c², where c is the longest side.

Front

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

Back

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

Front

If a rectangular pool measures 30 m by 40 m, how far is it diagonally across?

Back

Using the Pythagorean Theorem: c = √(30² + 40²) = √(900 + 1600) = √2500 = 50 m.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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