name: chapter 7: proportions and similarity lesson...

Name: Chapter 7: Proportions and Similarity

Lesson 7-1: Ratios and Proportions Date:

A is a comparison of two quantities using division.

Example:

can be used to compare three or more quantities.

Example 1:

a. The number of students who participate in sports programs at Central High School is 520. The total

number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.

b. The country with the longest school year is China, with 251 days. Find the ratio of school days to total

days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.)

Example 2: In ΔEFG, the ratio of the measures of the angles is 5:12:13. Find the measures of the angles.


Example 3:

A. Solve 6

18.2=

9

𝑦 B. Solve

4𝑥−5

3= −

26

6

Example 4: PETS Monique randomly surveyed 30 students from her class and found that 18 had a dog or a

cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog

or a cat.

Lesson 7-2: Similar Polygons Date:


Similar polygons have the same , but not necessarily the same .

Example 1: If 𝛥𝐴𝐵𝐶 ~ 𝛥𝑅𝑆𝑇, list all pairs of congruent angles and write a proportion that relates the

corresponding sides.

Example 2: Tanya is designing a new menu for the restaurant where she works. Determine whether the size

for the new menu is similar to the original menu. If so, write the similarity statement and scale factor.

Explain your reasoning.

A. Original: New: B. Original: New:


Example 3: The two polygons are similar.

A. Find x.

B. Find y.

Example 4: If 𝐴𝐵𝐶𝐷𝐸 ~ 𝑅𝑆𝑇𝑈𝑉, find the scale factor of 𝐴𝐵𝐶𝐷𝐸 to 𝑅𝑆𝑇𝑈𝑉 and the perimeter of each

polygon.


Lesson 7-3: Similar Triangles Date:

Example 1: Determine whether the triangles are similar. If so, write a similarity statement. Explain your

reasoning.

A. B.

Example 2: Determine whether the triangles are similar. If so, write a similarity statement. Explain your

reasoning.


A. B.

Example 2: MULTIPLE CHOICE If 𝛥𝑅𝑆𝑇 and 𝛥𝑋𝑌𝑍 are two triangles such that 𝑅𝑆

𝑋𝑌=

2

3, which of the

following would be sufficient to prove that the triangles are similar?

A. 𝑅𝑇

𝑋𝑍=

𝑆𝑇

𝑌𝑍 B.

𝑅𝑆

𝑋𝑌=

𝑅𝑇

𝑋𝑍=

𝑆𝑇

𝑌𝑍 C. ∠𝑅 ≅ ∠𝑆 D.

𝑅𝑆

𝑅𝑇=

𝑋𝑌

𝑋𝑍

Example 3: Given 𝑅𝑆̅̅̅̅ ∥ 𝑈𝑇̅̅ ̅̅ , 𝑅𝑆 = 4, 𝑅𝑄 = 𝑥 + 3, 𝑄𝑇 = 2𝑥 + 10, 𝑈𝑇 = 10, find 𝑅𝑄 and 𝑄𝑇.


Example 5: Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole

and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of

Sears Tower’s shadow and it was 242 feet at the same time. What is the height of the Sears Tower?


Lesson 7-4: Parallel Lines and Proportional Parts Date:

Example 1: In ∆𝑅𝑆𝑇, 𝑅𝑇̅̅ ̅̅ ∥ 𝑉𝑈̅̅ ̅̅ , 𝑆𝑉 = 3, 𝑉𝑅 = 8, and 𝑈𝑇 = 12. Find 𝑆𝑈.

Example 2: In ∆𝐷𝐸𝐹, 𝐷𝐻 = 18, 𝐻𝐸 = 36, and 𝐷𝐺 =1

2𝐺𝐹. Determine whether 𝐺𝐻̅̅ ̅̅ ∥ 𝐹𝐸̅̅ ̅̅ . Explain.


A of a triangle is a segment with endpoints that are midpoints of two sides of

the triangle.

Example 3: In the figure, 𝐷𝐸̅̅ ̅̅ and 𝐸𝐹̅̅ ̅̅ are midsegments of ∆𝐴𝐵𝐶.

A. Find 𝐴𝐵.

B. Find 𝐹𝐸.

C. Find 𝑚∠𝐴𝐹𝐸.


Example 4: In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances

in between city blocks. Find x.

Example 5: Find 𝑥 and 𝑦.


Lesson 7-5: Parts of Similar Triangles Date:

Example 1: In the figure, 𝛥𝐿𝐽𝐾 ~ 𝛥𝑆𝑄𝑅. Find the value of 𝑥.


Example 2: Sally’s arm is about 9 times longer than the distance between her eyes. She sights a statue across

the park that is 10 feet wide. If the statue appears to move 4 widths when she switches eyes, estimate the

distance from Sally’s thumb to the statue.

Example 3: Find 𝑥.


Lesson 7-6: Similarity Transformations Date:

Example 1: Determine whether the dilation from Figure A to Figure B is an enlargement or a reduction.

Then find the scale factor of the dilation.

A. B.

Example 2: A photocopy of a receipt is 1.5 inches wide and 4 inches long. By what percent should the

receipt be enlarged so that its image is 2 times the original? What will be the dimensions of the enlarged

image?


Example 3: Graph the original figure and its dilated image. Then verify that the dilation is a similarity

transformation.

A. original: M(–6, –3), N(6, –3), O(–6, 6)

image: D(–2, –1), F(2, –1), G(–2, 2)

B. original: G(2, 1), H(4, 1), I(2, 0), J(4, 0)

image: Q(4, 2), R(8, 2), S(4, 0), T(8, 0)

x

y

x

y


Lesson 7-7: Scale Drawings and Models Date:

A scale model or scale drawing is an object or drawing with lengths proportional to the object it

represents.

The scale of a model or drawing is the ratio of the length of the model or drawing to the actual length of

the object being modeled or drawn.

The scale factor of a drawing of model is the scale written as a unitless ratio in simplest form. They are

always written so that the drawing or model length comes first in the ratio.

Example 1: The distance between Boston and Chicago on a map is 9 inches. If the scale of the map is

1 inch: 95 miles, what is the actual distance from Boston to Chicago?

Example 2:

A. A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. What is the

scale of the model?

B. A miniature replica of a fighter jet is 4 inches long. The actual length of the jet is 12.8 yards. How many

times as long as the actual is the model jet?

Example 3: Gerrard is making a scale model of his classroom on an 11-by-17 inch sheet of paper. If the

classroom is 20 feet by 32 feet, choose an appropriate scale for the drawing and determine the drawing’s

dimensions.

name: chapter 7: proportions and similarity lesson...

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