Pythagorean Triples

Topic 8:
Right Triangles and Trigonometry

Day 1: The Pythagorean Theorem (Right Triangles)

Do Now:

1. Solve for the missing leg

​2. Solve for b

Theorem 8.1

The Pythagorean Theorems

Theorem 8.2 (converse)

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• Yes

• No

Multiple Choice

A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is the distance? Round your answer to the nearest whole number.

• 30 meters

• 83 meters

• 164 meters

• 260 meters

Multiple Choice

Find h

• 35.60
• 35.00
• 35.71
• 61.03

Let's work this together!

What is a Pythagorean Triple?

Some numbers seem to work perfectly in the Pythagorean Theorem, like 3, 4, and 5, which is 3² + 4² = 5². Sets of positive, whole numbers that work in the Pythagorean Theorem are called Pythagorean triples.

Most used Pythagorean Triples (write these down!)

• 3-4-5 (along with its multiples, example: 6-8-10)

• 5-12-13

• 8-15-17

• 7-24-25

• 9-40-41

• 11-60-61

Fill in the Blanks

Using the Pythagorean Triples, find the missing side (triangles are not always drawn to scale).

Fill in the Blanks

Using the Pythagorean Triples, find the missing side (triangles are not always drawn to scale).

Classifying Triangles

Classifying Right Triangles

• If c² = a² + b² --> ____ triangle

• If c² < a² + b² --> _____ triangle

• If c² > a² + b² --> _____ triangle

​Obtuse
Right
Acute

Which one is not a right triangle?

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Multiple Choice

• Acute

• Obtuse

• Right

• Not a Triangle

Multiple Choice

Which equation is set up correctly for this word problem?

• $$23^2+b^2=10^2$$

• $$10^2+b^2+23^2$$

• $$10^2+23^2=c^2$$

• $$a^2+23^2=c^2$$

Multiple Choice

• 43

• $$\sqrt{44.05}=6.6$$

• $$\sqrt{629}=25.1$$

• $$\sqrt{33}=5.74$$