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Discovering Geometry an Investigative Approach

Michael Serra

Chapter 11

Similarity - all with Video Answers

Educators

Section 1

Similar Polygons

01:17

Problem 1

Look at the rectangle at right. Find the ratio of the shaded area to the area of the whole figure. Find the ratio of the shaded area to the unshaded area.
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Jay Patel
Jay Patel
Numerade Educator
00:51

Problem 2

Use the figure below to find these ratios: $\frac{A C}{C D}, \frac{C D}{B D},$ and $\frac{B D}{B C}$

Jay Patel
Jay Patel
Numerade Educator
01:45

Problem 3

Consider these right triangles.
(IMAGE CAN'T COPY)
a. Find the ratio of the perimeter of $\triangle R S H$ to the perimeter of $\triangle M F L$
b. Find the ratio of the area of $\triangle R S H$ to the area of $\triangle M F L$

Erika Bustos
Erika Bustos
Numerade Educator
00:57

Problem 4

In Exercises $4-12,$ solve the proportion.
$\frac{7}{21}=\frac{a}{18}$

Jay Patel
Jay Patel
Numerade Educator
00:53

Problem 5

In Exercises $4-12,$ solve the proportion.
$\frac{10}{b}=\frac{15}{24}$

Jay Patel
Jay Patel
Numerade Educator
00:50

Problem 6

In Exercises $4-12,$ solve the proportion.
$\frac{20}{13}=\frac{60}{c}$

Jay Patel
Jay Patel
Numerade Educator
00:45

Problem 7

In Exercises $4-12,$ solve the proportion.
$\frac{4}{5}=\frac{x}{7}$

Jay Patel
Jay Patel
Numerade Educator
00:51

Problem 8

In Exercises $4-12,$ solve the proportion.
$\frac{2}{y}=\frac{y}{32}$

Jay Patel
Jay Patel
Numerade Educator
01:01

Problem 9

In Exercises $4-12,$ solve the proportion.
$\frac{14}{10}=\frac{x+9}{15}$

Jay Patel
Jay Patel
Numerade Educator
01:08

Problem 10

In Exercises $4-12,$ solve the proportion.
$\frac{10}{10+z}=\frac{35}{56}$

Jay Patel
Jay Patel
Numerade Educator
01:00

Problem 11

In Exercises $4-12,$ solve the proportion.
$\frac{d}{5}=\frac{d+3}{20}$

Jay Patel
Jay Patel
Numerade Educator
01:16

Problem 12

In Exercises $4-12,$ solve the proportion.
$\frac{y-1}{2 y+3}=\frac{4}{13}$

Jay Patel
Jay Patel
Numerade Educator
01:02

Problem 13

In Exercises $13-16$, use a proportion to solve the problem.
A car travels 106 miles on 4 gallons of gas. How far can it go on a full tank of 12 gallons?

Jay Patel
Jay Patel
Numerade Educator
02:07

Problem 14

In Exercises $13-16$, use a proportion to solve the problem.
Ernie is a baseball pitcher. He gave up 34 runs in 152 innings last season. What is Ernie's earned run average- the number of runs he would give up in 9 innings? Give your answer to the nearest hundredth of a unit.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:22

Problem 15

In Exercises $13-16$, use a proportion to solve the problem.
The floor plan of a house is drawn to the scale of $\frac{1}{4}$ in. $=1$ ft. The master bedroom measures 3 in. by $3 \frac{3}{4}$ in on the blueprints. What is the actual size of the room?

Erika Bustos
Erika Bustos
Numerade Educator
04:03

Problem 16

In Exercises $13-16$, use a proportion to solve the problem.
Altor and Zenor are ambassadors from Titan, the largest moon of Saturn. The sum of the lengths of any Titan's antennae is a direct measure of that Titan's age. Altor has antennae with lengths $8 \mathrm{cm}$ $10 \mathrm{cm}, 13 \mathrm{cm}, 16 \mathrm{cm}, 14 \mathrm{cm},$ and $12 \mathrm{cm}$ Zenor is
130 years old, and her seven antennae have an average length of $17 \mathrm{cm}$ How old is Altor?
(IMAGE CAN'T COPY)

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
03:15

Problem 17

If $\frac{a}{b}=\frac{r}{d},$ which of these statements are also true? Assume that $a, b, c,$ and $d$ are all nonzero values. For each proportion, use algebra to show it is true or give a counterexample to prove it is false.
a. $a d=b c$
b. $a c=b d$
c. $\frac{a}{c}=\frac{b}{d}$
d. $\frac{b}{a}=\frac{d}{c}$
e. $\frac{a}{d}=\frac{c}{b}$
f. $\frac{d}{b}=\frac{c}{a}$

Brittany Hull
Brittany Hull
Numerade Educator
02:20

Problem 18

The sequence $6,15,24,33,42, \ldots$ is an example of an arithmetic sequence - each term is generated by adding a constant, in this case $9,$ to the previous term. The sequence $6,12,24,48,96, \ldots$ is an example of a geometric sequence - each term is generated by multiplying the previous term by a constant, in this case 2 . Find the missing terms assuming each pattern is an arithmetic sequence, and then find the missing terms assuming each pattern is a geometric sequence.
a. $10,\text{_}, 40,...$
b. $2,\text{_}, 50,...$
c. $4,\text{_}, 36,...$

Brittany Hull
Brittany Hull
Numerade Educator
01:04

Problem 19

Consider the pattern $10, x, 40, \ldots$
a. If the pattern is an arithmetic sequence, the value of $x$ is called the arithmetic mean of 10 and $40 .$ Use your algebra skills to explain how to calculate the arithmetic mean of any two numbers.
b. If the pattern is a geometric sequence, the positive value of $x$ is called the geometric mean of 10 and $40 .$ Use your algebra skills to explain how to calculate the geometric mean of any two positive numbers.
c. For any two positive numbers, the ratio of the smaller number to their geometric mean is equal to the ratio of the geometric mean to the larger number. Find the formula for the geometric mean of $a$ and $b$ by solving the proportion $\frac{a}{c}=\frac{c}{b}$ for $c$ Are there any values for which this formula isn't true?
d. Use this formula to find the geometric mean of 2 and $50,$ and of 4 and 36

Angela Guo
Angela Guo
Numerade Educator