Pythagorean Theorem 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 distance between two points (A and B) on a coordinate plane?

Back

To find the distance between two points A(x1, y1) and B(x2, y2), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

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

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: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

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 (legs) equals the square of the longest side (hypotenuse).

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths a, b, and c can form a right triangle, check if 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 ramp is 15.7 inches long and forms a right triangle with a height of 12 inches, what is the base length?

Back

Using the Pythagorean Theorem: c² = a² + b²; 15.7² = 12² + b²; b = √(15.7² - 12²) = 9.8 inches.

Front

What is the significance of the diagonal in a rectangle?

Back

The diagonal of a rectangle can be calculated using the Pythagorean Theorem, as it forms two right triangles within the rectangle.