Similarity Review

Similarity Review

By Eugene Foley

​We would name these triangles so corresponding vertexes line up!

​Sides of ~ Triangles are Proportional

​

​

​A

​B

​C

​~

​

​D

​E

​F

​- Eugene Foley

Remember when we have an unknown side, we have to set up proportions and use our algebra skills to solve for x!

Poll

If ABC and DEF are similar, what is the correct set up to solve for x?

• $$\frac{13}{21}=\frac{27}{x}$$  

• $$\frac{21}{13}=\frac{x}{27}$$  

• $$\frac{13}{27}=\frac{21}{x}$$  

• $$\frac{x}{13}=\frac{27}{21}$$  

Dilations

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​

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Produce Similar Figures​

​Non-rigid Motion

1) Reflection

2) Rotation

3) Translation

​

Preserve size​

​Rigid Motions

Transformations

Multiple Choice

Looking at the composition of Transformations, what do we do first?

• Rotation

• Reflection

• Translation

• Dilation

Dilations make a figure larger or smaller.

To find out the scale factor we divide corresponding sides by each other (make sure the image is in the numerator)​

​

​Some text here about the topic of discussion.

​Dilation!

​

Poll

What is the scale factor if ZXY is the image?

• $$\frac{3}{4}$$  

• $$12$$  

• $$4$$  

• $$3$$  

How do we find the new coordinates when dilating?

Lets us k=-2 and a point (3,-2)​

Multiple Choice

What is the coordinate of the image of the point (2,-2) dilated by a scale factor of $$\frac{3}{2}$$  ?

• (6,-4)

• (-3,3)

• (4,-4)

• (3,-3)

Multiple Choice

Choose the correct scale factor:

• 2
• 3
• 1/3
• 1/2

Multiple Choice

The point A (8, 12) was dilated to become point A' (2, 3). What was the scale factor?

• ½

• ¼

• 4

• 2

Multiple Choice

A dilation produces a congruent figure

• True

• False

Multiple Choice

When the scale factor of a dilation is less than one, the dilation is a reduction.

• True
• False

Multiple Choice

What can you say about the scale factor, k?

• k > 1

• k = 1

• 0 < k < 1

​There are three similarity criteria

​Angle-Angle

​

• ​When two angles are congruent

​Side-Side-Side

​

• Corresponding sides have the same proportion​

​Side-Angle-Side

​

• Two sides are proportional and the included angle is congruent​

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

Multiple Choice

ΔSQR∼ΔSPT. Which choice below lists two corresponding sides?

• SP and SR

• QS and PT

• PS and RS

• TP and RQ

Multiple Choice

If two figures are similar their angles are______.

• proportional
• congruent
• supplementary
• complementary

Multiple Choice

Give the reason for similarity

• AA

• SAS

• SSS

• Not similar

Multiple Choice

If the triangles are similar, state how.

• SSS

• SAS

• AA

• Not similar

Multiple Choice

If the triangles are similar, state why.

• AA

• SAS

• SSS

• Not similar

Multiple Choice

Are these triangles similar?
Known angles in Triangle 1:  40⁰,60⁰
Known angles in Triangle 2:  80⁰,40⁰

• Yes
• No
• There is not enough information to decide.

Multiple Choice

Solve for x. The two figures are similar.

• x = 6
• x = 9
• x = 7
• x = `0

• Perimeter increases by the scale factor​

• Area increases by the square of the scale factor​

​

​Some text here about the topic of discussion.

​Area and Perimeter Proportions

​

Multiple Choice

An NBA basketball court (rectangle) is similar to an elementary school basketball court. The sideline of the NBA court  is 94 feet, and the sideline of the elementary court is 84.6 feet. The NBA court has a perimeter of 288 ft. Find the perimeter of the elementary court.

• 288 feet
• 5802 feet
• 259 feet
• 275 feet

Multiple Choice

An NBA basketball court (rectangle) is similar to an elementary school basketball court. The sideline of the NBA court  is 94 feet, and the sideline of the elementary court is 84.6 feet. The NBA court has an area of 4700 square feet. Find the area of the elementary court.

• 4700 square feet
• 5,802 square feet
• 5,222 square feet
• 3807 square feet

​Partitioning a Line Segment

• Find the coordinates of the "starting" point

• Determine the change in x and y (Direction is important)

• Multiply by Part/Whole

• Add these amounts to the x and y starting coordingates​

Some text here about the topic of discussion

Multiple Choice

6) The ratio is 3:1. How many parts are there?

• 2

• 3

• 4

• 5

Multiple Choice

Determine the ratio of the directed line segment AB when partitioned by point P.

• 1:2

• 2:1

• 1:1

• 3:1

• 1:4

Multiple Choice

Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3.

The coordinates of the point P are:

• (1,5)

• (0,4)

• (3, 1)

• (-1, 1)

• Connects Midpoint to midpoint

• Midsegments are parallel to the third side and are half the length

​Midsegments

• Connects a Vertex to the opposite midpoint

• All medians meet​ at the centroid which separates the median 2:1

Medians

Midsegments and Medians

Some text here about the topic of discussion

Multiple Choice

• A

• B

• C

• D

Multiple Choice

$$\overline{AC}\ \parallel\ _{ }$$  ____

• $$\overline{LK}$$  

• $$\overline{LJ}$$  

• $$\overline{JK}$$  

• The segment is not parallel to any other segment in the diagram.  

Multiple Choice

What is the perimeter of  $$\Delta ABC$$  ?

• 13

• 14

• 26

• Cannot be determined from the information given.  

Multiple Choice

What is the value of x?

• 1

• 2

• 4

• Impossible to determine from the information given.