Course Assessment Review

Dilations

Multiple Choice

What does the scale factor do in a dilation?

• Tells you how much the image grows or shrinks

• Tells you what the center of dilation is

• There's not enough information here to answer this

• Nothing, it's unnecessary information

Scale Factors are just as they sound

• Factors (multipliers) that scale (change the size of) a shape

• Scale factors can do one of two things: grow or shrink an object

• A scale factor larger than one (>1) makes an object get larger --> could be a fraction or a whole number

• A scale factors smaller than one (<1) makes an object get smaller

Multiple Select

Which scale factors would increase an image?

• $$\frac{3}{2}$$

• $$\frac{1}{2}$$

• $$3.5$$

• $$\frac{2}{1}$$

• 5
  

Multiple Select

Which scale factors shrink an image?

• $$0.5$$

• $$\frac{3}{4}$$

• $$1$$

• $$\frac{2}{1}$$

• $$\frac{3}{2}$$

Multiple Select

What are the properties of dilations?

• Changes the size of an object

• Changes the shape of an object

• Changes one side but not the others

• Changes all the sides equally

• Changes angle measures

Proportion Example

How do we solve a proportion now?

Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

Does the image show a Dilation and what is the scale factor?

• Yes; k = 2

• Yes; k = 1/2

• No, it's a translation.

• No, it's a reflection.

Multiple Choice

If a line segment has a length of 12 units and after a dilation the image length is 4 units, what was the scale factor?

• 3

• 1/3

• 8

• 16

Sequences of Transformations (Rigid Motions)

Example

    

The blue trapezoid is translated 4 units right and then reflected over the x-axis to form the red trapezoid.

Multiple Choice

What sequence of transformations maps the red parallelogram to the green parallelogram?

• A translation followed by a reflection.

• A rotation followed by a translation.

• A reflection followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

What sequence of transformations will get you from the blue triangle BCD to the red triangle B"C"D"?

• Rotation, then Rotation

• Rotation, then Dilation

• Reflection, then Rotation

• Translation, then Reflection

Multiple Choice

What sequence of transformations could map triangle ABC to triangle A"B"C"?

• A dilation followed by a rotation.

• A translation followed by a reflection.

• A rotation about the origin followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflection followed by a rotation.

• Rotation followed by a translation.

• Reflection across the x-axis followed by a reflection across the y-axis.

• Translation followed by a rotation.

Triangle Similarity:

AA, SSS, and SAS

By Heather Eve

Similarity Postulate 1: AA

--> AA means "Angle Angle"

--> Two triangles with the SAME EXACT angle next to one other SAME EXACT angle will be similar to each other.

​

(but not necessarily identical)​

​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA

• Similar by AA

Multiple Choice

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA.

• Similar by AA

Similarity Postulate 2: SSS

--> SSS means "Side Side Side"

-->This one is different from congruence SSS!!! A triangle with a set of THREE sides that each have the SAME proportion to another triangle's matching sides.

​

​

​

Subject | Subject

Some text here about the topic of discussion

Similarity Postulate 2: SSS

EXAMPLE!

​​

​ Each set of matching sides has the same proportion!

​

2/1 from left to right

1/2 from right to left​​

​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

State if the triangles are similar by SSS.

• Similar but not SSS

• Not Similar

• Yes, by SSS

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similar but not SSS

• Not Similar

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similiar but not SSS

• Not similar

Similarity Postulate 3: SAS

--> SSS means "Side Angle Side"

-->This one is different from congruence SAS!!! It is also the trickiest one. It goes like this:

​

*Two triangles with a matching pair of sides that have a certain proportion.

*Next to that side each triangle has an angle that is EXACTLY the same!

*Next to that angle both triangles have a side that is the same proportion as their first proportion!​​

​

Subject | Subject

Some text here about the topic of discussion

Similarity Postulate 3: SAS

EXAMPLE!

​​

​ AB/DF--> 12/8 = 3/2 (first set of sides)

​

50=50 (identical angle)

​

CB/FE--> 24/16 = 3/2 (second set of sides)​

​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Multiple Choice

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Multiple Choice

State if the triangles are similar by SAS.

• Similar but not SAS

• Yes, SAS Similarity

• Not Similar

Proportionality Theorems

Multiple Choice

If a line divides two sides of a triangle proportionally, then it is .......

• congruent to the third side.

• parallel to the third side

• perpendicular to the third side.

• twice the length of the third side

Multiple Choice

Find the length of $$\overline{AB}$$  

• 8

• 5

• 6

• 4

Multiple Choice

Find the length of AB

• 9

• 12

• 13

• 15

Multiple Choice

Determine whether $$\overline{QR}\parallel\overline{ST}$$  

• Yes, the lines are parallel

• No, the lines are not parallel

Multiple Choice

Find the length of $$\overline{DF}$$  .

• 6

• 8

• 7.2

• 6.8

Multiple Choice

If $$\overline{BE}\parallel\overline{CF}$$  find the distance between point E and point F.

• 244

• 302

• 256

• 300

Multiple Choice

Find the value of z.

• 21

• 40

• 34

• 52

Multiple Choice

Find the value of "a".

• 9

• 12

• 18

• 40

Multiple Select

Select ALL of the following ratios that are true.

• $$\frac{x}{9}=\frac{10}{15}$$  

• $$\frac{9}{15}=\frac{x}{10}$$  

• $$\frac{x}{15}=\frac{10}{9}$$  

• $$\frac{10}{9}=\frac{15}{x}$$  

Finding Missing Sides Using Trig Ratios

​

Multiple Choice

Which trig ratio would you use to solve for x?

• Sine

• Cosine

• Tangent

Fill in the Blanks

Find x and round to the nearest thousanths.

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14
• sin(33)=x/14
• cos(33)=14/x
• sin(33)=14/x

Fill in the Blanks

Solve for x. Round to the nearest tenth.

Fill in the Blanks

Solve for x. Round to the nearest tenth if needed.

Arc Length & Area of a Sector Reteach

Objective: Use proportional reasoning to find arc length and area of a sector

Arc Length

Ex 1: Find the length of the minor arc

Area of a Sector

Multiple Choice

Find the arc length of arc AB.

• 12.57 units
• 75.40 units
• 24 units
• 125.66 units

Multiple Choice

Find the estimated area of the shaded area.

• 10.732 units squared
• 100.53 units squared
• 9.75 units squared
• 3,015.93 units squared

Multiple Choice

Find the area of the shaded space.

• 113.10 units squared
• 150.80 units squared
• 157.82 units squared
• 10.92 units squared

Multiple Choice

Stephanie is cutting a pie. Stephanie's mother wants one fourth of the pie. The diameter is 20 cm. What is the sector area of the pie her mother does not want?

• 235.62 cm squared
• three fourths of the pie
• 78.54 cm squared
• 83.99 cm squared

Multiple Choice

Segment ED is tangent to circle O. What is the value of x?

• 232

• 52

• 79

• 115

Multiple Choice

Assume both lines are tangent to circle O. What is the value of x?

• 90

• 115

• 120

• 45

Fill in the Blanks

ST is a tangent to ⨀Q.  Find the value of r

​Tangent- Chord Theorem

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Fill in the Blanks

$BC\ is\ \tan gent\ to\ the\ circle.\ Find\ m\angle CBD$

​Theorem

Tangent segments which form a common external point are congruent.

Fill in the Blanks

JK is tangent to circle L at K and JM is tangent to circle L at M. Find the value of x

Fill in the Blanks

JK is tangent to circle L at K and JM is tangent to circle L at M. Find the value of x

Multiple Select

• $$\angle FDE$$  

• $$\angle DAC$$  

• $$\angle BAC$$  

• $$\angle BAE$$  

• $$\angle ACD$$  

Multiple Choice

State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.

• A

• B

• C

• D

Multiple Choice

State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.

• A

• B

• C

• D

Multiple Choice

• 70

• 140

• 35

• 88

Multiple Choice

• m∠K=100 & m∠M=100

• m∠K=50 & m∠M=50

• m∠K=100 & m∠M=50

• m∠K=50 & m∠M=100

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• 7

• 44

• 8