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 is expressed as: a² + b² = c².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the Hypotenuse.

Front

What type of triangle has all angles less than 90 degrees?

Back

An Acute Triangle.

Front

What type of triangle has one angle greater than 90 degrees?

Back

An Obtuse Triangle.

Front

What type of triangle has one angle equal to 90 degrees?

Back

A Right Triangle.

Front

Given sides a = 2.1, b = 7.2, c = 7.5, is this a right triangle?

Back

Yes, it is a right triangle because it satisfies the Pythagorean theorem: 2.1² + 7.2² = 7.5².

Front

If a triangle has sides of lengths 9, 8, and 7, what type of triangle is it?

Back

It is an Acute Triangle.

Front

What is the converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if a² + b² = c², where c is the longest side.

Front

What is the relationship between the sides of an obtuse triangle?

Back

In an obtuse triangle, the square of the length of the longest side is greater than the sum of the squares of the lengths of the other two sides.