WEEK 33-PROPORTIONALITY-ON-GEOMETRIC-SHAPES

Proportionality on Geometric Shapes

Start

Objectives

Proportionality Problems

Summary

Practice

Similar Triangles

Proportionality

Proportionality

Ham Bread

The proportion is kept

That is:

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

🗨️

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

Says that

For instance the equation:

Similar Triangles

Lenghts:

Angles:

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

Example 1: Consider triangles ABC and DEF:

Proportional sides

Equal Angles

In general, similarity of Triangles is denoted as follows:

Proportionality Problems

EF=4

DF=10

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

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

Let's see some examples:

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

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.

Try it by Yourself

05:00

Practice

FlipCard Quiz

Start

The sum of angles in the polygon below is:

1/5

The operations performed on the picture are:

2/5

Select the scale factor in the image below.

3/5

Select the hypothenuse in the right triangle.

4/5

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

5/5

End of the quiz!

HOW DID YOU DO IT?

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

Summary

8TH-PROPORTIONALITY-ON-GEOMETRIC-SHAPES-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.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.