Geo Unit 4 Final Exam Review

​Unit 4 Final Exam Review
Scale Factor & Similar Triangles & Polygons

By Darryl Padgett

The Scale Factor

• We use the scale factor(sf) to help describe and determine the type of dilation that takes place

• If sf > 1; the dilation is an enlargement

• is sf < 1; the dilation is a reduction

• if sf = 1; the image and pre-image are the exact same

Labelling

Label the diagram.

Drag labels to their correct position on the image

enlargement

scale factor

change in size

reduction

be distorted

stays the same

Multiple Select

Which of the following algebraic rules represents an enlargement?
Select all that apply

***There's more than 1 correct answer!

• $$(x,y)\ \rightarrow\ (1.6x,1.6y)$$  

• $$(x,y)\ \rightarrow\ (0.75x,0.75y)$$  

• $$(x,y)\ \rightarrow\ (\frac{18}{5}\ x,\ \frac{18}{5}\ y)$$  

• $$(x,y)\ \rightarrow\ (-x,y)$$  

Multiple Select

Which of the following algebraic rules represents a reduction?
Select all that apply

***There's more than 1 correct answer!

• $$(x,y)\ \rightarrow\ (3x,3y)$$  

• $$(x,y)\ \rightarrow\ (\frac{3}{4}x,\ \frac{3}{4}​y\ )$$  

• $$(x,y)\ \rightarrow\ (0.99x,0.99y)$$  

• $$(x,y)\ \rightarrow\ (5x,\ 5y)$$  

​Find the scale factor used to create the scale factor

​Scale Factor = new divided by the old.

​​​First identify the corresponding/ similar sides in the figures.

• ​ EX: Side GH which is 8cm corresponds to side G'H' which is 10 cm.

​Take any of the matching sides and divide the new measure by the old measure.

• ​Notice how the new image is larger than the pre-image. This is because the Scale factor is greater than 1.

​

Multiple Choice

Triangle ABC will be dilated by a scale factor of 1/2.  What will be the coordinates of C'?

• (-1, -2.5)
• (12, 6)
• (3, -1.5)
• (0, 1.5)

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's a reduction; the scale factor is 2.
• It's an enlargement; the scale factor is 2.
• It's an enlargement; the scale factor is 1/2.
• It's a reduction; the scale factor is 1/2.

Multiple Choice

Enlargement or reduction?  Find the scale factor!

• It's an enlargement; the scale factor is 3.
• It's a reduction; the scale factor is 1/3.
• It's a reduction; the scale factor is 1/2.
• It's an enlargement; the scale factor is 2. 

By Darryl Padgett

Multiple Choice

Find side length X.

• 16
• 18
• 2.4
• 15

Match

Match the following based upon the figure.

• $$\angle A\ \cong\angle$$

• Adjacent Angles are $$\angle B\ \cong\angle$$

• Sim $$\angle C\ \cong\angle$$ ilar Triangles are

X

Y

Z

• X

• Y

• Z

Multiple Choice

What is the value of x?

• 12

• 14

• 16

Multiple Choice

The pair of figures are similar.

Find the missing side.

• x = 20
• x = 12
• x = 5
• x = 4

​Solving Similar Polygons

​Similar Polygons

​ABCD ~ EFGH

Corresponding Angles

​

​

​Corresponding Sides

Multiple Choice

The two figures are similar. What is their perimeter ratio? The first

Write your answer as a simplified fraction.

•  2

• $$0.55$$  

• $$\frac{10}{20}$$  

• $$2.5$$  

• $$\frac{25}{100}$$  

Multiple Choice

Are the following similar? Why or why not?

• Yes
• No, the corresponding angles are not equal.
• No, the ratios of the corresponding sides are not equal.

Multiple Choice

Solve for x.

• 21
• 14
• 12
• 18

Match

Based upon the diagram match the items.

• $$\frac{AB}{?}$$

• $$\frac{BC}{?}$$

• $$\frac{AC}{?}$$

DE

EF

DF

• DE

• EF

• DF