Day 89 - 8.MG.4 Pythagorean Theorem Word Problems

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

How do you find the distance between two points using the Pythagorean Theorem?

Back

To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, use the formula: Distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Front

What are the legs and hypotenuse in a right triangle?

Back

In a right triangle, the legs are the two sides that form the right angle, while the hypotenuse is the side opposite the right angle and is the longest side.

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

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 greater than 90 degrees.

Front

What is a right triangle in terms of angle measures?

Back

A right triangle is defined as having one angle that measures exactly 90 degrees.

Front

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

Back

To determine if a triangle is obtuse, check if the square of the longest side is greater than the sum of the squares of the other two sides: c² > a² + b².

Front

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

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: a² + b² = c².