Pythagorean Theorem and it's 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: c² = a² + b².

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that 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 can you determine if a triangle is obtuse using the Pythagorean Theorem?

Back

If c² > a² + b² for the sides of a triangle, then the triangle is obtuse.

Front

How can you determine if a triangle is acute using the Pythagorean Theorem?

Back

If c² < a² + b² for the sides of a triangle, then the triangle is acute.

Front

What is the longest side of a right triangle called?

Back

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

Front

If a triangle has sides of lengths 2, 12, and 13, what type of triangle is it?

Back

The triangle is obtuse because 13² > 2² + 12².

Front

If Lisa drives 46 km south and 13 km east, how do you find the distance from her starting point?

Back

Use the Pythagorean Theorem: Distance = √(46² + 13²) = 47.8 km.

Front

What is the formula to find the length of the missing side in a right triangle?

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse.

Front

If one side of a right triangle is 5 cm and the other is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = 13 cm.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).