4B Review (Pythagorean Thm)-P4

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.

Front

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

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. Rearrange the formula based on which side is missing: - If c is missing: c = √(a² + b²) - If a is missing: a = √(c² - b²) - If b is missing: b = √(c² - a²).

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 in a right triangle?

Back

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

Front

If a triangle has sides measuring 8 mm, 15 mm, and 17 mm, is it a right triangle?

Back

Yes, it is a right triangle because 8² + 15² = 17² (64 + 225 = 289).

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

Can three squares with side lengths 3, 4, and 5 form a right triangle?

Back

Yes, they can form a right triangle because 3² + 4² = 5² (9 + 16 = 25).

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 a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Front

What is the formula for calculating the area of a right triangle?

Back

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