Pythagorean Theorem & Converse

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

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

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

Back

To determine if three side lengths can form 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

If the legs of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

The hypotenuse is 10, calculated using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so √100 = 10.

Front

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

Back

The area of a right triangle can be found using 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, where 1 is the length of the side opposite the 30-degree angle.

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 5, 12, and 13, is it a right triangle?

Back

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

Front

What is the length of the diagonal of a rectangle with sides 3 and 4?

Back

The length of the diagonal is 5, calculated using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so √25 = 5.