WEEK 33-PROPORTIONALITY-ON-GEOMETRIC-SHAPES

Proportionality on Geometric Shapes

Objectives

Start

Proportionality

Similar Triangles

Proportionality Problems

Practice

Summary

Proportionality

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

For instance the equation:

🗨️

Says that

As bread (labeled as x) increases ham shoud increase (labeled as x).

Ham Bread

That is:

The proportion is kept

Similar Triangles

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

Angles:

Example 1: Consider triangles ABC and DEF:

Lenghts:

In general, similarity of Triangles is denoted as follows:

Equal Angles

Proportional sides

Proportionality Problems

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.

EF=4

DF=10

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

05:00

Practice

FlipCard Quiz

Start

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

End of the quiz!

HOW DID YOU DO IT?

Summary

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

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-PROPORTIONALITY-ON-GEOMETRIC-SHAPES-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.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 multiple ways." 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.