01 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

How can you determine if three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).

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 measuring more than 90 degrees.

Front

What does it mean if no triangle can be formed with given lengths?

Back

If no triangle can be formed, it means that the lengths do not satisfy the Triangle Inequality Theorem, meaning the sum of the lengths of any two sides is not greater than the length of the third side.

Front

If a triangle has sides of lengths 4, 7, and 10, what type of triangle is it?

Back

It is an obtuse triangle.

Front

If a triangle has sides of lengths 4, 6, and 7, what type of triangle is it?

Back

It is an acute triangle.

Front

If a triangle has sides of lengths 4, 7, and 11, can a triangle be formed?

Back

No, a triangle cannot be formed with these lengths.

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.