WEEK 33-PROPORTIONALITY-ON-GEOMETRIC-SHAPES

Objectives

Start

Proportionality on Geometric Shapes

1

2

Proportionality

Similar Triangles

Practice

Summary

Proportionality Problems

Proportionality

Go back to menu

For instance the equation:

Says that

As bread (labeled as x) increasesham shoud increase (labeled as x).

🗨️

Proportionality refers to the relationship between two quantities where their ratio remains constant.

1

That is:

The proportion is kept

HamBread

Go back to menu

Similar Triangles

Go back to menu

Example 1: Consider triangles ABC and DEF:

Definition: Two triangles are similar if corresponding angles are equal and corresponding sides are in proportion.

Angles:

Lenghts:

Their angles are equal among each other:

The ratio of their corresponding side lengths is constant.

When angle is the same we put a tick | on the angle.

In general, similarity of Triangles is denoted as follows:

Equal Angles

Proportional sides

When angle is the same we put a tick | on the angle.

Proportionality Problems

Go back to menu

Let's see some examples:

Example 1: The triangles ▲ABC and ▲DEF are similar. Find side EF.

Example 2: The triangles ▲ABC and ▲DEF are similar. Find the hypothenuse DF.

DF=10

EF=4

1. State each proportions for each triangle.

2. Replace each value on the proportionality equation.

3.Find the unknown by cross multiplication (or just looking the fractions)

State the proportion between the two triangles and solve using cross multiplication:

State the proportion between the two triangles and solve using cross multiplication:

1. State the proportions for each triangle.

2. Find the unknown (which in this case is a leg)

3. With two legs, find the hypothenuse.

4. Find squares of legs, sum up, then apply the square root.

05:00

Try it by Yourself

A ramp forms a right triangle with ground and loading dock. Ramp is 20 m long and touches the ground 16 m from the dock.

If ramp is shortened to 10 m, and put on the same parallel as before, find the new distance from ground to dock. -> Fill the table

Go back to menu

Practice

Go back to menu

Start

FlipCard Quiz

1/5

The sum of angles in the polygon below is:

2/5

The operations performed on the picture are:

3/5

Select the scale factor in the image below.

4/5

Select the hypothenuse in the right triangle.

5/5

Distance between points (1,1) and (7,9) is

HOW DID YOU DO IT?

End of the quiz!

Summary

Similar triangles have the same shape(same angles) and mantain their proportions

Go back to menu

Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

8TH-PROPORTIONALITY-ON-GEOMETRIC-SHAPES-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

It is highly advised to have:

MATERIAL

• 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.2 Understand similarity and congruence using models and transformations.MA.8.GR.2.4 Solve mathematical and real-world problems involving proportional relationships between similar triangles."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.K12.MTR.1.1 Actively participate in effortful learning both individually and collectively.MA.K12.MTR.7.1 Apply mathematics to real-world contexts.MA.K12.MTR.2.1 "Demonstrate understanding by representing problems in multipleways."ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.MA.K12.MTR.5.1 Use patterns and structure to help understand and connect mathematical concepts.