Lesson 8.1: Pythagorean Theorem

Pythagorean Theorem

• Pythagorean Theorem:

Practice

• What is the length of each missing side?

SOL Question

• What is the length of theunlabeled side?

Reducing Radicals

• Reducing Radicals:

• Ex: Reduce each radical:√45 √12 √72

Practice

Reduce each radical:√12 = √18 =

√25 = √50 =

√27 = √20 =

√28 = √63 =

√75 = √1 =

√8 = √6 =

Practice

Practice

• Find the missing side length of each triangle. Put solutions in simplest radical form.

4m 6m 10m

5m

Application

ABCD represents a lawn with a sidewalk. How much shorter is walking across the lawn from A to D than walking along the sidewalk?

A B

C D100m

300m

Converse of the Pythagorean Theorem

Converse of the Pythagorean Theorem:

Right:

Acute:

Obtuse:

Practice

Extension – Possible Side Length

• Ex: A triangle has side lengths 6 and 8. What must the third side be for a right triangle?

• A triangle has side lengths 5 and 12. What must the third side be for an obtuse triangle?

Classwork

• Lesson 8.1, #1 – 14

Special Right Triangles (part 1)

• 45 – 45 – 90 Triangle:

Practice

• What is the length of each missing side?

5m12m

Challenge

• Find the length of AC.

45o

45o

18m

36m

A B C

D

Bonus: Pythagorean Triples

• Pythagorean Triples:

Homework

• Lesson 8.1 #17 – 35 oddLesson 8.2, #7 – 11 odd

• Lesson 8.2, #15 – 33 odd