Topic Test 3 & 4 Review Lesson Part 2

​Topic Test 3 & 4 Review Lesson Part 2

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Multiple Choice

Which of these angles is NOT congruent to angle 5? #1

• Angle 6
• Angle 8
• Angle 1
• Angle 4

Multiple Choice

Line l and m are cut by transversal n. Which statement proves that line l is parallel to line m? #3

• ∠2 ≅ ∠3; Vertical Angles are Congruent

• ∠2 ≅ ∠8; Same Side Exterior Angles Are Congruent

• m∠7 + m∠8 = 180°; Linear Pair Thm.

• m∠3 + m∠5 = 180°; Same Side Interior Angles are Supplementary

Match

Use the diagram below to identify the given angle pairs. #10

• A. Vertical Angles

• B. Corresponding Angles

• C. Alternate Interior Angles

• D. Same - Side Interior Angles

• E. Supplementary Angles

∡2 & ∡3

∡2 & ∡6

∡4 & ∡5

∡4 & ∡6

∡6 & ∡8

• ∡2 & ∡3

• ∡2 & ∡6

• ∡4 & ∡5

• ∡4 & ∡6

• ∡6 & ∡8

Fill in the Blanks

In the diagram, parallel lines l and k are cut by transversal p. The measure of angle 5 is 138°. What is $m\angle3+m\angle6$   ? *** #6

 

Multiple Choice

Line l and m are cut by transversal n. Which statement proves that line l is parallel to line m? #3

• ∠2 ≅ ∠3; Vertical Angles are Congruent

• ∠2 ≅ ∠8; Same Side Exterior Angles Are Congruent

• m∠7 + m∠8 = 180°; Linear Pair Thm.

• m∠3 + m∠5 = 180°; Same Side Interior Angles are Supplementary

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Multiple Choice

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong?

• Eric should have started by putting the compass needle point at the midpoint of the segment AB.

• On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

• Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

• Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

Multiple Choice

Which one is the correct construction for a perpendicular bisector?

• 1
• 2
• 3
• 4

Fill in the Blanks

On a coordinate plane, the position of two friends can be defined by the points A(2,5) and B(8,8). Their teacher is standing at point C, and the teacher's distance from point A is twice the distance from point B. What is the y coordinate of point C? #9

Match

Consider the following figures given in the first row and match these figures with the correct name for the pair of angles shown in the figure. #12

Alternate interior angles

Alternate exterior angles

Corresponding angles

Vertical angles

• Alternate interior angles

• Alternate exterior angles

• Corresponding angles

• Vertical angles

Multiple Choice

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong? #13

• Eric should have started by putting the compass needle point at the midpoint of the segment AB.

• On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

• Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

• Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

Multiple Choice

What geometric construction is shown in the diagram below? #15

• an angle bisector

• a line parallel to a given line

• an angle congruent to a given angle

• a perpendicular bisector of a segment

Properties of Sequences of Rigid Motions

• Size and shape stay the same.

• Angle measures stay the same.

• Area and perimeter stay the same.

• Parallel segments or lines stay parallel.

• Pre-image and image are congruent.

Multiple Choice

What type of rotation does this represent (from red to blue)? #19

• 270⁰ clockwise

• 360⁰

• 90⁰ counterclockwise

• 180⁰

Multiple Select

Which transformation rules create an image where distance is preserved? (the size/shape doesn't change) Select all that apply. #17

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

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

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

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

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

Multiple Select

What dilation of scale factor can be used to create an image that is CONGRUENT to its pre-image? Check all that apply. #18***

• Scale factor of 3.

• Scale factor of 1/3.

• Scale factor or -2.

• Scale factor of 1.

• Scale factor of -1.

Multiple Choice

Which rule was used to translate trapezoid DEFG to trapezoid D'E'F'G'? #22 ***

• $$\left(x,\ y\right)\rightarrow\left(x\ -\ 4,\ y\ +\ 4\right)$$

• $$\left(x,\ y\right)\rightarrow\left(x\ +\ 4,\ y\ +\ 4\right)$$

• $$\left(x,\ y\right)\rightarrow\left(x\ -\ 4,\ y\ -\ 4\right)$$

• $$\left(x,\ y\right)\rightarrow\left(x\ +\ 4,\ y\ -\ 4\right)$$

Multiple Choice

Which of the following shows a rotation 90 degrees counterclockwise about the origin and then a translation  $$\left(x,\ y\right)\rightarrow\left(x\ -\ 2,\ y\ -\ 5\right)$$  ?

#21 ***

Multiple Choice

A triangle has vertices (-4,3), (6,9), and (2,-3). The triangle is reflected across the y-axis and then translated 1 unit up and 4 units right. Which of the following will be the coordinates of a vertex of the image after both transformations? #26

• (4,7)

• (-2,2)

• (-2,9)

• (2,-2)

Multiple Choice

Triangle FXY is rotated and then translated to a

new location and named triangle ABC. Which of the

following is true? #29

• ΔFXY is congruent to ΔABC because only rigid

  motions were performed.

• ΔFXY is congruent to ΔABC because non-rigid

  motions were performed.

• ΔFXY is not congruent to ΔABC because only

  rigid motions were performed.

• ΔFXY is not congruent to ΔABC because non-

  rigid motions were performed.

Multiple Select

On a coordinate plane, a single transformation will

be performed on square RSTU.

Select three transformations of square RSTU that

would result in a congruent figure. #30

• a translation 3 units up and 8 units to the right

• a rotation of 270° counterclockwise about the

  origin

• a dilation by a scale factor of 1 with respect to

  the origin

• a dilation by a scale factor of 1.5 with respect to

  the origin

• a dilation by a scale factor of −2 with respect to

  the origin

Directed Line Segment Formula

Remember to use Order of Operation

Multiple Choice

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K with JP/KP = 1/5? $$x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1;\ y=\left(\frac{m}{m+n}\right)\left(y_2-y_1\right)+y_1$$  #32

• (–13, –3)

• (–7, –1)

• (–5, 0)

• (17, 11)

Multiple Choice

Which representation of a transformation on a coordinate grid does not preserve congruence? #33

• (x, y) ⟶ (y, -x)

• (x, y) ⟶ (-x , -y)

• (x, y) ⟶ (x +2, y ⎯ 3

• (x, y) ⟶ ( 3x, 3y)

Multiple Choice

Find the coordinates of the point on the directed line segment from J to K that partitions JK with J being 2/3 of the way to K. #34

• (-1, -2)

• (1, 1)

• (-0.6, -1.4)

• (0.6, 0.4)

Multiple Choice

Points C, D, and E are collinear on segment CE, and CD/CE = 3/8. C(1,3) and E(8, 4). What are the coordinates of D? #35

• (6.6 , 3.8)

• (29, 7)

• (-4.6, 2.2)

• ( 3.63, 3.38)

Multiple Choice

Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'? #43

• a dilation with a scale factor less than 1 and then a reflection

• a dilation with a scale factor less than 1 and then a translation

• a dilation with a scale factor greater than 1 and then a reflection

• a dilation with a scale factor greater than 1 and then a translation