Pythagorean Theorem

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). This can be expressed as c² = a² + b².

Front

How can you determine if a triangle is obtuse, acute, or right using the Pythagorean Theorem?

Back

You can determine the type of triangle by comparing the squares of the sides: If c² = a² + b², the triangle is right; if c² > a² + b², the triangle is obtuse; if c² < a² + b², the triangle is acute.

Front

What is the definition of an obtuse triangle?

Back

An obtuse triangle is a triangle in which one of the angles is greater than 90 degrees.

Front

What is the definition of an acute triangle?

Back

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

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle because 5² = 3² + 4² (25 = 9 + 16).

Front

If a triangle has sides of lengths 7, 8, and 10, what type of triangle is it?

Back

It is an obtuse triangle because 10² > 7² + 8² (100 > 49 + 64).

Front

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

Back

It is a right triangle because 13² = 5² + 12² (169 = 25 + 144).

Front

If a triangle has sides of lengths 6, 8, and 10, what type of triangle is it?

Back

It is a right triangle because 10² = 6² + 8² (100 = 36 + 64).

Front

If a triangle has sides of lengths 9, 12, and 15, what type of triangle is it?

Back

It is a right triangle because 15² = 9² + 12² (225 = 81 + 144).