Review topic test Transformations and Congruence

Review topic test Transformations and Congruence

by Alina Sanchez Mederos

Multiple Choice

Identify the geometric term.

• point
• line
• ray
• line segment

Multiple Choice

Identify the geometric term.

• ray
• line segment
• line
• point

Multiple Choice

Identify the geometric term.

• line
• ray
• point
• line segment

Multiple Choice

Identify the geometric term.

• line
• ray 
• point
• line segment

Multiple Choice

Where do the three lines meet?

• F
• B
• D
• A

Multiple Choice

Name the geometric figure.

• $$\overrightarrow{CD}$$

• $$\overrightarrow{DC}$$

• $$\overline{CD}$$

Multiple Choice

Name the geometric figure.

• Segment PR

• Ray PR

• Line PR

• Plane PR

Multiple Choice

Name the geometric figure.

• Ray T

• Plane T

• Line T

• Sheet of paper

Multiple Choice

Name the geometric figure.

• $$\angle ABD$$

• $$\angle BAD$$

• $$\angle ADB$$

• $$\overrightarrow{AB}$$

Multiple Choice

Name the geometric figure.

• $$1$$

• V1

• $$\overrightarrow{1}$$

• $$\angle1$$

Multiple Choice

Name the geometric figure.

• $$\overrightarrow{TS}$$

• $$\overrightarrow{ST}$$

• $$\overline{ST}$$

• $$\overleftarrow{ST}$$

Multiple Choice

What does this drawing indicate?

• $$\overline{DG}\ \ \parallel\ \ \overline{KT}$$

• $$\overline{DG\ }\ \perp\ \overline{KT}$$

• $$JT\ \cong KJ$$

Fill in the Blanks

Find the length indicated.

Fill in the Blanks

Find the length indicated.

Multiple Choice

Write an equation that could be used to relate the lengths shown.

• 4 + 3x + 2 = 7x - 2

• 7x - 2 + 4 = 3x + 2

• 7x - 2 + 3x + 2 = 4

Multiple Choice

Solve

• 50°
• 58°
• 115°
• 226°

Multiple Choice

Solve

• x = 6
• x = 7
• x = 12
• x = 144

Multiple Choice

Find TM and MS given that M is the midpoint of the segment.

• TM = 15, MS = 15

• TM = 7.5, MS = 7.5

• TM = 7.5, MS = 15

• TM = 15, MS = 7.5

Multiple Choice

Line l bisects the segment. Find the value of x.

• x = 15

• x = 6

• x = 9

• x = 3

Multiple Choice

Line l bisects the segment. Find the value of x.

• x = 15

• x = 6

• x = 9

• x = 3

Multiple Choice

Identify the smallest angle of rotation that maps the image to itself.

$$Use\ \ the\ \ formula\ \ \frac{360\degree}{n}$$ Use the number of edges as n. 

• 90°

• 180°

• 45°

• 60°

Multiple Choice

How many lines of symmetry does this shape have?

This a regular octogon, an 8 sided figure.

• 2

• 4

• 6

• 8

Multiple Choice

What are the angles of rotation for a square?

• multiples of 30

• multiples of 45

• multiples of 90

• multiples of 180

Multiple Choice

How many lines of symmetry are there on a rhombus?

• 0

• 1

• 2

• 4

Multiple Choice

Identify the smallest angle of rotation that maps the image to itself.

• 72°
• 180°
• 144°
• 45°

Multiple Choice

Symmetrical?

• Is symmetrical

• not symmetrical

Multiple Choice

Find the distance between the points (4, 3) and (0, 6).

• 3
• 4
• 5
• 7

Multiple Choice

Find the y-coordinate of the midpoint of the line

• 1
• 2
• -2
• 3

Multiple Choice

Find the length of line segment AB given A(4, 3) and B(0, 6).

• 3
• 4
• 5
• 7

Multiple Choice

How far is point A from point B?

• 7.1
• 7.8
• 8.7
• 8.9

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Describing Rigid Motions Using Coordinate Notation​

​Some transformations preserve length and angle measure, and some do not. A rigid motion (or isometry) is a transformation that changes the position of a figure without changing the size or shape of the figure. Translations, reflections, and rotations are rigid motions.

​

​q Rotations and translations also preserve orientation. This means that the order of the vertices of the preimage and image are the same, either clockwise or counterclockwise.

q Reflections do not preserve orientation.

Multiple Choice

Point M (-3, 5) is translated using this rule. 
(x, y) ----> (x - 1, y) 
What are the coordinates of M'?

• (-4, 5)
• (-2, 5)
• (-4, 4)
• None of these

Multiple Choice

How is triangle ABC being translated to triangle A'B'C'?

• up 3, left 8
• up 9, left 4
• down 3, right 8
• down 9, right 4

Multiple Choice

Translations, reflections and rotations are all known as ________________________.

• Geometry
• Rigid Transformations
• Congruent
• Non- Rigid Transformations

Multiple Choice

When a figure is translated the post-image in  always _______ to the pre-image 

• Congruent
• Bigger
• Smaller
• Rotated

Multiple Choice

Which transformation is NOT a rigid motion (the size changes)?

• reflection
• rotation
• dilation
• translation

Multiple Choice

A rigid motion ...

• preserves size and location
• preserves shape and location
• preserves size and shape
• makes the figure larger

Multiple Choice

Which answer shows a reflection across the y-axis?

• a
• b
• c
• d

Multiple Choice

Identify the transformation from A to D.

• 90^o Clockwise Rotation
  270^o Counter Clockwise Rotation
• 180^o Rotation
• 270^o Clockwise Rotation
  90^o Counter Clockwise Rotation
• 360^o Rotation

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• 90^o clockwise rotation
• 90^o counter clockwise rotation
• Reflection across the y-axis
• Reflection across the x-axis

Multiple Choice

Relfect the image over the y-axis and then translate it 4 to the right and down 3.  Which quadrants will the image be located in?

• Quadrant I and II
• Quadrant II and III
• Quadrant III and IV
• Quadrant I and IV

Multiple Choice

Which sequence of transformations will result from shape F to its image shape F''?

• Reflection over both axes

• Reflection, then rotation

• Translation, then reflection

• Rotation, then translation

Multiple Choice

What sequence of transformations will map trapezoid A to its image A'?

• Reflection, then translation

• Rotation, then translation

• Reflection, then rotation

• Rotation, then dilation

Multiple Choice

Which series of transformations were performed in the figure?

• Translation 5 units down, reflection over the y-axis

• Reflection over the x-axis, translation 6 units right

• Rotation 90^o clockwise, reflection over the x-axis

• Rotation 180^o clockwise, reflection over the y-axis

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees cw around the origin

• Rotate 90 degrees cw around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees ccw about the origin.

Multiple Choice

Which sequence of transformations occurred to pentagon QRSTU to form its image Q"R"S"T"U"?

• Translation, then a reflection over the y-axis.

• Reflection over the x-axis, then a translation.

• Rotation, then a reflection over the y-axis.

• Reflection over the y-axis, then a translation.

Multiple Select

Which transformation rules create an image where distance is preserved? (the size/shape doesn't change) Select all that apply.

• $$\left(x,\ y\right)\rightarrow\left(-x,\ y\right)$$

• $$\left(x,\ y\right)\rightarrow\left(2x,\ 2y\right)$$

• $$\left(x,\ y\right)\rightarrow\left(x+3,\ y\right)$$

• $$\left(x,\ y\right)\rightarrow\left(-y,\ x\right)$$

• $$\left(x,\ y\right)\rightarrow\left(0.4x,\ 0.4y\right)$$

Multiple Choice

Describe the transformations that map ABC onto A"B"C"

• translate 5 up and 1 left then reflect over y
• translate 5 down and 1 left, then reflect over y
• reflect over y=x then translate left 8
• reflect over x then rotate 90 clockwise

Multiple Choice

What is the ordered pair for the final location of P( 2, 3) after this series of transformations? $$\left(x,y\right)\rightarrow\left(x+2,\ y-4\right)$$  then reflected over the  $$y-axis?$$  

• $$P'\left(-4,\ 1\right)$$  

• $$P'\left(-4,\ -1\right)$$  

• $$P'\left(1,\ -4\right)$$  

• $$P'\left(-1,\ -4\right)$$  

Multiple Choice

What does CPCTC stand for?

• Congruent parts of congruent triangles are congruent
• Corresponding parts of congruent triangles are congruent
• Corresponding parts of corresponding triangles are corresponding
• Corresponding parts of congruent triangles are Canadian.

Multiple Choice

Fill in the blank.

• Given
• Reflexive Property
• Transitive Property
• They're the same side!!!!!! 

Multiple Choice

What additional information is required to prove the two triangles are congruent by ASA?

• A)
• B)
• C)
• D)

Multiple Choice

If ∆LMK ≅ ∆LMT, then
∠K ≅ ____

• T
• ∠T
• ∠M
• ∠L

Multiple Choice

These two triangles are congruent. If ∠C is 40^o find the measure of ∠F.

• 40^o
• 50^o
• 90^o
• 45^o

Multiple Choice

Name the corresponding angle or side.

• A
• B
• C
• D

Multiple Choice

Identify the missing statement or reason

• Reflexive Property

• Definition of Midpoint

• Given

• Vertical Angles Theorem

Multiple Choice

 ∠A = ≅

• ∠M
• ∠N
• ∠L

Multiple Choice

If ∆PIG ≅ ∆COW, WO≅?

• GI

• PI

• PG