Exploring Proportions in Similar Figures

This video tutorial covers the concept of proportions and their application in geometry, focusing on similar figures and indirect measurement. It explains how to solve for unknown side lengths in similar triangles using proportions and demonstrates real-life applications, such as measuring heights using shadows. The tutorial also discusses the use of scale models to understand proportions better.

What does the squiggly symbol (~) represent in geometry?

• Equal to

• Similar to

• Congruent to

• Parallel to

If triangle ABC is similar to triangle DEF, which of the following is true?

• Side BC is proportional to side DF

• Angle A is congruent to angle D

• Side AB is proportional to side DE

• Angle B is congruent to angle F

Given that BC = 16, EF = 12, AB = 10, and DE = x, what is the value of x?

• 6

• 8

• 7

• 7.5

If BC = 16, EF = 12, AC = x, and DF = 18, what is the value of x?

• 18

• 22

• 20

• 24

A girl who is 5 feet tall casts a 3-foot shadow. If a building casts a 15-foot shadow, how tall is the building?

• 30 feet

• 25 feet

• 20 feet

• 35 feet

A man who is 6 feet tall casts a 3.5-foot shadow. If a flagpole casts a 17.5-foot shadow, how tall is the flagpole?

• 30 feet

• 25 feet

• 35 feet

• 20 feet

What is the proportion used to find the height of a building using the shadow of a girl?

• Girl's shadow / Building's shadow = Girl's height / Building's height

• Girl's shadow / Building's height = Girl's height / Building's shadow

• Girl's height / Building's shadow = Girl's shadow / Building's height

• Girl's height / Building's height = Girl's shadow / Building's shadow

What is the proportion used to find the height of a flagpole using the shadow of a man?

• Man's shadow / Flagpole's shadow = Man's height / Flagpole's height

• Man's shadow / Flagpole's height = Man's height / Flagpole's shadow

• Man's height / Flagpole's shadow = Man's shadow / Flagpole's height

• Man's height / Flagpole's height = Man's shadow / Flagpole's shadow

If a giant heart is 14 feet tall and the giant person is 170 feet tall, what is the expected height of a heart for a 6-foot tall man?

• 0.4 feet

• 0.5 feet

• 1 foot

• 0.6 feet

A scale model of a building is 6 inches tall with a scale of 1 inch = 50 feet. How tall is the actual building?

• 300 feet

• 250 feet

• 400 feet

• 350 feet