Exploring Proportions and Similar Polygons

The video tutorial covers the concept of proportions and their application to similar polygons. It begins with an introduction to ratios and proportions, explaining how to write and simplify them. The tutorial then demonstrates solving proportions using cross multiplication. It further explores the application of proportions in similar polygons, discussing the concept of scale factor. Finally, it explains how to calculate the areas of similar shapes by squaring the side ratios.

What is a ratio?

• A comparison of three quantities

• A comparison of two quantities

• A sum of two quantities

• A product of two quantities

How can you write the ratio of 8 inches to 1200 inches in simplest form?

• 1:150

• 8:1200

• 1:100

• 8:150

What is a proportion?

• Two ratios set equal to each other

• A product of two ratios

• A sum of two ratios

• A ratio divided by another ratio

If 2/10 = x/50, what is the value of x?

• 20

• 5

• 10

• 25

Given a triangle with a perimeter of 72 inches and side ratios of 3:4:5, what is the length of the longest side?

• 30 inches

• 18 inches

• 24 inches

• 36 inches

What does it mean for two polygons to be similar?

• They have congruent angles and proportional sides

• They have equal side lengths

• They have the same area

• They have the same perimeter

If triangle PET is similar to triangle LOG with a scale factor of 2, and PE = 5, what is the length of LO?

• 5

• 10

• 15

• 20

How do you find the scale factor between two similar shapes?

• By creating a ratio of corresponding side lengths

• By dividing the areas of the shapes

• By adding the side lengths of the shapes

• By comparing the perimeters of the shapes

When calculating the area of similar shapes, what must you do to the side ratios?

• Square them

• Double them

• Halve them

• Cube them

If the area of a smaller rectangle is 84 square meters and the side ratio is 7:21, what is the area of the larger rectangle?

• 756 square meters

• 588 square meters

• 336 square meters

• 252 square meters