Pythagorean Theorem & Converse Flashcard

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 is expressed as a² + b² = c².

Front

In a right triangle, how do you identify the hypotenuse?

Back

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

Front

If a right triangle has legs of lengths 7 and 24, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 7² + 24² = 49 + 576 = 625, so c = √625 = 25.

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

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

Back

To find a missing side, use the Pythagorean Theorem: a² + b² = c², where you can solve for the missing side.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

If a triangle has sides of lengths 40, 30, and 50, is it a right triangle?

Back

Yes, because 40² + 30² = 1600 + 900 = 2500 = 50².

Front

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

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

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.

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 each leg.