Pythagorean Review

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

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

Back

To determine if a triangle is a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides. If c² = a² + b² holds true, then the triangle is a right triangle.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three interior angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one interior angle greater than 90 degrees.

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side. The other two sides are called the legs, and they form the right angle.

Front

How do you find the length of an unknown side in a right triangle?

Back

To find the length of an unknown side in a right triangle, use the Pythagorean theorem: c² = a² + b². Rearrange the formula to solve for the unknown side.

Front

What is the formula to calculate the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean theorem.

Front

How can you verify if a triangle with sides 20, 21, and 28 is acute?

Back

To verify if the triangle is acute, check if the square of the longest side (28) is less than the sum of the squares of the other two sides: 28² < 20² + 21².

Front

What is the difference between a right triangle and an acute triangle?

Back

A right triangle has one angle that is exactly 90 degrees, while an acute triangle has all angles less than 90 degrees.