Pythagorean Theorem and its 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

How do you classify a triangle with side lengths 5, 12, and 13?

Back

This triangle is a right triangle because it satisfies the Pythagorean Theorem: 5² + 12² = 13² (25 + 144 = 169).

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

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, it is a right triangle because 7² + 24² = 25² (49 + 576 = 625).

Front

What is the length of the hypotenuse in a right triangle with legs of lengths 6 and 8?

Back

The length of the hypotenuse is 10, calculated using the Pythagorean Theorem: 6² + 8² = c² (36 + 64 = 100, so c = 10).

Front

What are the side lengths 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 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.