# 8.9 - Pythagorean Theorem

8.9  The student will

a)  verify the Pythagorean Theorem;

b)  apply the Pythagorean Theorem.

### BIG IDEAS

• I can determine what size TV to purchase, figure what length ladder will be needed for a job, and find the shortest route to travel.
• I will calculate the length of a segment and determine a right angle without directly measuring.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - 8.9 Understanding

·  The Pythagorean Theorem is essential for solving problems involving right triangles.

·  The relationship between the sides and angles of right triangles are useful in many applied fields.

·  In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the legs. This relationship is known as the Pythagorean Theorem: a2 + b2 = c2.

·  The Pythagorean Theorem is used to determine the measure of any one of the three sides of a right triangle if the measures of the other two sides are known.

·  The converse of the Pythagorean Theorem states that if the square of the length of the hypotenuse equals the sum of the squares of the legs in a triangle, then the triangle is a right triangle.  This can be used to determine whether a triangle is a right triangle given the measures of its three sides.

·  Whole number triples that are the measures of the sides of right triangles, such as (3, 4, 5),
(6, 8, 10), (9, 12, 15), and (5, 12, 13), are commonly known as Pythagorean triples.

·  The hypotenuse of a right triangle is the side opposite the right angle.

·  The hypotenuse of a right triangle is always the longest side of the right triangle.

·  The legs of a right triangle form the right angle.

### ESSENTIALS

• How can the area of squares generated by the legs and the hypotenuse of a right triangle be used to verify the Pythagorean Theorem?
For a right triangle, the area of a square with one side equal to the measure of the hypotenuse equals the sum of the areas of the squares with one side each equal to the measures of the legs of the triangle.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  8.9b1  Determine whether a triangle is a right triangle given the measures of its three sides.

·  8.9a1  Verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement.

·  8.9b2  Determine the measure of a side of a right triangle, given the measures of the other two sides.

·  8.9b3  Solve practical problems involving right triangles by using the Pythagorean Theorem.

### KEY VOCABULARY

right triangle, leg, hypotenuse, Pythagorean Theorem

Updated: Nov 20, 2018