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

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

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 units.

Front

What is the length of the diagonal of a rectangle with a width of 8 inches and a height of 6 inches?

Back

Using the Pythagorean Theorem: 8² + 6² = c²; 64 + 36 = c²; 100 = c²; c = 10 inches.

Front

How do you find the area of a square?

Back

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

Front

If the area of a square is 36 in², what is the length of one side?

Back

To find the side length, take the square root of the area: side = √36 = 6 inches.

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. The shortest side is opposite the 30° angle.

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 hypotenuse is √2 times the length of one leg.

Front

If a right triangle has a hypotenuse of 10 units and one leg of 6 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8 units.

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a rectangular pool measures 30 m by 40 m, what is the distance across the pool diagonally?

Back

Using the Pythagorean Theorem: 30² + 40² = c²; 900 + 1600 = c²; 2500 = c²; c = 50 m.