WEEK 31-RIGHT-TRIANGLES-AND-THE-PYTHAGOREAN-THEOREM

Right Triangles and The Pythagorean Theorem

Start

Objectives

The Pythagorean Theorem

Summary

Exercises and Applications

Right Triangles

Story

Story

Right Triangles

Example 1: This is a right triangle:

Definition: A triangle with one angle that measures exactly 90° (a right angle)

What is a Right Triangle?

The Pythagoream Theorem

Pythagorean theorem states the relationship between the lengths of the sides of a right triangle.

🗨️

a b

is the hypothenuse lenght .

are the lenght of the sides.

a²+b²=c²

Theorem: The sum of the squared legs of a right triangle equals to the hypothenuse squared.

a=3, b=4, c=5

a, b, and c

a²+b²=c²

The property is verified

Example 1: Determine if a triangle with sides 6, 8, and 10 is a right triangle.

Property: If , then the triangle with sides is a right triangle.

Is it a Right Triangle?

a=5, b=12, c=?

a= 0.8 units

a=0.6, b=?, c=1

c=13

Example 2: Find the hypothenuse in the triangle shown below.

Example 1: If one side a = 0.6 units and the hypotenuse c = 1 units, find b.

Let's see some examples:

Exercises and Applications

a=8 meter

a=6, b=?, c=10

Solution

Click here to draw >

how high does the ladder reach?

A ladder leaning against a wall forms a right triangle. If the ladder is 10 meter long and the bottom of the ladder is 6 meter from the wall,

Reaching the Roof with a Ladder

Click here to draw >

The solution will appear in 60 seconds

• 3, 4, 5 -----> Yes
• 2, 2, 3 -----> No
• 5,6,7 -----> No
• 5,12,13 -----> Yes

No

Yes

5,12,13

5,6,7

2, 2, 3

3, 4, 5

Determine if the three lenghts can form a right triangle or not.

Summary: Right Triangles

8TH-RIGHT-TRIANGLES-AND-THE-PYTHAGOREAN-THEOREM-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

See you next time

Great job!

A journey soon begin through Social Science experiences!

Welcome 6th graders!

• Grid paper.
• A Protactor.
• Pencils of different colors.
• Eraser.
• A rule.

• A compass.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

MATERIAL

It is highly advised to have:

"MA.8.GR.1 Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles." MA.8.GR.1.1 Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles. MA.8.NSO.1 Solve problems involving rational numbers, including numbers in scientific notation, and extend the understanding of rational numbers to irrational numbers. MA.8.NSO.1.7 Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.