Similarity and Scale Factor Review

What 2 things must be true in order for 2 figures to be similar?

• their corresponding angles are equal

• their corresponding sides are proportional

• the angles in one figure are all the same 

• the sides are equal 

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

A spotlight is placed on the ground 30 feet from the wall of a building. A 6 foot tall person stands 8 feet from the light source, between it and the wall. A shadow is cast on the wall. How tall is the shadow on the wall?

• 22.5 ft

• 16.5 ft

• 22 ft

• 15 ft

Answer explanation

$\frac{tall}{shadow}=\frac{6\ ft}{8ft}=\frac{y}{30\ ft}$

Tags

CCSS.HSG.SRT.B.5

• 4

• 12

• -12

Answer explanation

larger (SF) = smaller
16x = 4
divide by 16

Tags

CCSS.7.G.A.1

Find the value of m. Type the numerical value in the blank. (Do not type m = )

Answer explanation

$\frac{10}{15}=\frac{12}{m}\ is\ one\ correct\ way$

Tags

CCSS.HSG.SRT.A.2

• 1.25

• 8

Answer explanation

large (SF) = small
10x = 8
divide by 10

Tags

CCSS.7.G.A.1

Are the polygons similar?

Explain how you know.

• yes - corresponding angles are the same and the sides are equivalent ratios

• no - the angles match up, but the sides are not proportional

• no - the angles do not correspond correctly

• yes - the angles are equal and the sides are the same

Answer explanation

Similar polygons must have :

1) corresponding angles equal

AND

2) corresponding sides proportional (equal ratios)

Tags

CCSS.HSG.SRT.A.2

The length of a rectangle is 12 inches. A scale factor of 1.5 is applied to the length. What is the new length of the rectangle?

• 18 inches

• 8 inches

• 1/8 inches

• 13.5 inches

Answer explanation

original length (SF) = new length

Tags

CCSS.7.G.A.1

• A

• B

• C

• D

• all will equal the same answer

Answer explanation

Check the cross products of each one

A map has a scale of 1 inch: 125 feet. How many actual feet does 4 inches represent on the map?

• 500 ft

• 31.25 ft

• 250 ft

Answer explanation

$\frac{1\ in\ }{125\ ft}=\frac{4\ in}{x}$

Tags

CCSS.7.G.A.1

The perimeter of a polygon is 90 inches. If a scale factor of 2.5 is used to increase the size of the polygon, what is the new perimeter?

• 225 in.

• 36 in

• 500 in.

Answer explanation

$P_1\ \cdot\ SF\ =\ P_2$

$90\ \cdot\ \left(2.5\right)\ =\ new\ perimeter$

Tags

CCSS.7.G.A.1