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). Formula: 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 one side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Front

If a triangle has sides of lengths 10, 12, and 13, what type of triangle is it?

Back

It is an acute triangle.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c², where c is the longest side, then the triangle is a right triangle.

Front

What is the area of a square with a side length of 15?

Back

Area = side² = 15² = 225.

Front

Given the sides 4, 5, and 6, what type of triangle is formed?

Back

It is an acute triangle.

Front

Which set of side lengths does not form a right triangle: 14, 15, 29 or 38, 80, 90?

Back

14, 15, 29 does not form a right triangle.

Front

What is the relationship between the angles in an acute triangle?

Back

All angles in an acute triangle are less than 90 degrees.

Front

What is the relationship between the angles in a right triangle?

Back

One angle in a right triangle is exactly 90 degrees.

Front

What is the relationship between the angles in an obtuse triangle?

Back

One angle in an obtuse triangle is greater than 90 degrees.