# MA6-WEEK33-COMBINED-PROBLEM-SOLVING-OF-RATIOS-AND-GEOMETRY

VIMSCHOOL

Created on June 24, 2024

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## Transcript

Objectives

Start

Combined Problem Solving of Ratios and Geometry

Story

Area of ▲ and ▮

1

2

Practice

Summary

Similar Figures

Story

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Area of ▲ and ▮

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Try it by yourself:

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Triangle Area: It's half of the rectangle's area

Height

Base

Let's see some examples:

Example 1: Find the area of a triangle with a height of 3 and a base of 8.

Example 2: Find the area of the triangle △ABC shown in the figure

Area=12

Area=9

Area of rectangle=base*height =6*3 =18 Area of triangle= half of the rectangle's area =18/2 =9

Similar Figures

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Similar triangles are triangles that have the same shape but may differ in size.

For instance the triangles:▲ABC and ▲DEF

are similar triangles (proportional)

Similar triangles mantain proportions between their sides.

The proportion holds:

Superposing the previous triangles:

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 hypotenuse DF.

DF=10

EF=4

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

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

Practice

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Try it by yourself:

05:00

Try it by Yourself

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

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Summary

Similar triangles have the same shape and mantain their proportions

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

6TH-COMBINED-PROBLEM-SOLVING-OF-RATIOS-AND-GEOMETRY-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

It is highly advised to have:

MATERIAL

- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- Geogebra installed on your phone/tablet/computer (or use online version).

Standard 2: Model and solve problems involving two-dimensional figures and three-dimensional figures.MA.6.GR.2.1 Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangleMA.6.GR.2.2 Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectanglesStandard 3: Understand ratio and unit rate concepts and use them to solve problems.MA.6.AR.3.5 Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.