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

Right Triangles and The Pythagorean Theorem

Objectives

Start

Story

Right Triangles

The Pythagorean Theorem

Exercises and Applications

Summary

Story

Right Triangles

What is a Right Triangle?

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

Example 1: This is a right triangle:

The Pythagoream Theorem

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

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

🗨️

a²+b²=c²

are the lenght of the sides.

a b

is the hypothenuse lenght .

Is it a Right Triangle?

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

a²+b²=c²

a, b, and c

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

a=3, b=4, c=5

The property is verified

Let's see some examples:

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.

a=5, b=12, c=?

a=0.6, b=?, c=1

a= 0.8 units

c=13

Exercises and Applications

Click here to draw >

Reaching the Roof with a Ladder

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,

how high does the ladder reach?

a=6, b=?, c=10

a=8 meter

Solution

Click here to draw >

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

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

The solution will appear in 60 seconds

3, 4, 5

2, 2, 3

Yes

5,6,7

No

5,12,13

Summary: Right Triangles

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

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

MATERIAL

It is highly advised to have:

• 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).

"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.