4) Pythagorean Theorem STAAR 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

What is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are of equal length, and the hypotenuse is √2 times the length of one leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the shorter leg.

Front

How can the Pythagorean Theorem be used in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the distance between two points, constructing buildings, and in navigation.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula, which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane, is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

What is an example of a Pythagorean triple?

Back

An example of a Pythagorean triple is (3, 4, 5), where 3² + 4² = 5².