4B Review (Pythagorean Thm)-P7

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: c² = a² + b².

Front

What is a right triangle?

Back

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

Front

How can 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 (hypotenuse) is equal to the sum of the squares of the other two sides.

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

What does the term 'converse' refer to in the context of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Front

If a triangle has sides measuring 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5² + 12² = 13² (25 + 144 = 169).

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 the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

Calculate the diagonal of a rectangle with width 50 yards and length 100 yards.

Back

The diagonal can be calculated using the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √(12500) ≈ 111.8 yards.

Front

What set of sides can form a right triangle?

Back

The sides 5, 12, and 13 can form a right triangle because 5² + 12² = 13².

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √(100) = 10.