Geometry Toolkit: 4, 5, & 6 Lesson 2022-2023

​Geometry Toolkit: 4, 5, & 6 Lesson 2022-2023

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Multiple Choice

In the figure, triangle PQR has vertices P(0, −1), Q(3, −1) and R(5, −3). What are the vertices of the image after the translation (x, y) → (x − 5, y + 1)? #1

• P′ (1, −6), Q′ (4, −6), R′ (6, −8)

• P′ (−5, 0), Q′ (−2, 0), R′ (0, −2)

• P′ (5, −2), Q′ (8, −2), R′ (10, −4)

• P′ (−1, 4), Q′ (2, 4), R′ (4, 2)

Multiple Choice

The dashed figure is the image of the solid figure. What is the Algebraic Notation for the Translation? #2

• (x, y) → (x - 7, y + 4)

• (x, y) → (x + 7, y - 4)

• (x, y) → (x + 4, y + 7)

• (x, y) → (4x, 7y)

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Multiple Choice

∆QRS contains the points: Q(4, 2) R(5, 1) S(3,7). If the triangle is reflected across the x-axis, what will Q' be? #11

• Q'(4, 2)

• Q'(-4, 2)

• Q'(-4, -2)

• Q'(4, -2)

Multiple Choice

Reflect the point (2, -4) over the y-axis. #12

• (-4, 2)

• (-2, 4)

• (-2, -4)

• (2, 4)

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Multiple Select

Match the description with the graph shown below. (Hint: There are two correct answers) #13

• $$90\degree\ clockwise\ rotation$$

• $$180\degree\ clockwise\ rotation$$

• $$90\degree\ counterclockwise\ rotation$$

• $$180\degree\ counterclockwise\ rotation$$

Multiple Select

Match the description with the graph shown below. (Hint: There are two correct answers) #14

• $$90\degree\ clockwise\ rotation$$

• $$90\degree\ counterclockwise\ rotation$$

• $$270\degree\ clockwise\ rotation$$

• $$270\degree\ counterclockwise\ rotation$$

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Multiple Choice

The coordinates of triangle JRB are J(1, -2), R(-3, 6), and B(4, 5). What are the coordinates of the vertices of its image after the transformation over the y-axis, (x, y) → (–x, y), then a translation of (x, y) → (x + 2, y – 1)? #3

• (3, 1), (-1, -7), (6, -6)

• (3, -3), (-1, 5), (6, 4)

• (1, -3), (5, 5), (-2, 4)

• (-1, -2), (3, 6), (-4, 5)

Multiple Choice

Given: A(-5,-1), L(-3, -2) and T(-3, 2). First, translate 6 units right and 3 units down. Then reflect the image over the y-axis,(x, y) → (–x, y). What are the coordinates for A''B''C''? #4

• A''(1, -4) L''(-3, -5) T''(-3, -1)

• A''(-1, -4) L''(-3, -5) T''(-3, -1)

• A''(-1, 4) L''(-3, -5) T''(-3, 1)

• A''(1, -4) L''(3, -5) T''(3, -1)

Multiple Choice

Which composition of similarity transformations maps LMN to L'M'N'? #20

• 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

Multiple Choice

Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'? #21

• 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

Multiple Choice

Find the image of the $$\Delta$$  with vertices  $$P\left(-1,5\right),\ Q\left(-4,3\right),\ R\left(-2,1\right)$$  after the similarity transformation: 

Rotation 180 degrees about the origin AND Dilation:  $$\left(x,y\right)\rightarrow\left(2x,2y\right)$$   #18

• $$P''\left(-10,1\right),\ Q''\left(-6,\ 8\right),\ R''\left(-2,\ 4\right)$$  

• $$P''\left(5,-1\right),\ Q''\left(3,-4\right),\ R''\left(1,-2\right)$$  

• $$P''\left(1,-5\right),\ Q''\left(4,-3\right),\ R''\left(2,-1\right)$$  

• $$P''\left(2,-10\right),\ Q''\left(8,-6\right),\ R''\left(4,-2\right)$$  

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. #28

• 45°

• 90°

• 180°

• 360°

Math Response

Find the value of x.*** #65

EXTERIOR ANGLE= REMOTE INTERIOR ANGLE 1 + REMOTE INTERIOR ANGLE 2

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

Solve for x.

HINT!!! THE SUM OF THE ANGLES EQUALS 180 DEGREES. #29

Type answer here

Correct Answer: -11

Deg^°

Rad

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent. #27

• SSS

• SAS

• ASA

• Not Possible

Multiple Choice

Are these triangles congruent? If so, state the rule which you used to determine congruence. (Select all that apply). #9

• SAS

• SSS

• Both SSS and SAS

• Not necessarily congruent

Multiple Choice

What is Reason F? #31

• SSS Congruence

• SAS Congruence

• ASA Congruence

• AAS Congruence

• HL Congruence

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Multiple Choice

Triangle JKL is an isosceles triangle, where ∠J is the vertex angle, m∠J = 40°

and m∠L = (5x + 20)°. What is the value of x? #5

• 10

• 14

• 24

• 12

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Multiple Choice

Which pair(s) of sides are parallel? #35

• AB and BC

• AB and CD

• AD and BC

• AD and DA

Multiple Choice

Complete the proof to show that ABCD is a parallelogram.    $$\overline{BC}\parallel\overline{AD}\ and\ \overline{CD}\parallel\overline{BA}\ and\ because$$ the ____________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

#37

• lengths of consecutive sides are not equal

• slopes of opposite sides are equal

• lengths of opposite sides are equal

• slopes of consecutive sides are not equal

Multiple Choice

In the image, side AB has a slope of -3 and AD has a slope of 1/3. What does this mean is true? #36

• Side AB and AD are parallel

• Side AB and AD form a right angle

• Side AB and AD are congruent

• Nothing Specific

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Multiple Choice

Fill in the blank:

A perpendicular bisector is perpendicular to and passing through the ___________________ of a segment. #40

• endpoint

• corner

• midpoint

• side

Math Response

Suppose line m is the perpendicular bisector of  $$\overline{AB}$$  . Find the value of x. #42

Type answer here

Correct Answer: 8

Deg^°

Rad

Math Response

Find the value of x. #44

Type answer here

Correct Answer: 4

Deg^°

Rad

Multiple Choice

Write the equation of the perpendicular bisector of the line AB given: A(1,3) & B(-3,5) #45

• y = 2x + 4

• y = 2x + 6

• y = -2x + 6

• y = 2x - 6

Math Response

Find x if LI = 3x + 9 and IA=15 #48

HINT!!! USE THE CENTROID RATIO THEOREM

2(SHORTER PART OF MEDIAN) =(LARGER PART OF MEDIAN)

Type answer here

Correct Answer: 7

Deg^°

Rad

Math Response

Find the x value of the centroid of a triangle whose vertices are (1, 10) (-7, 2), and (-3, 7). #49

Type answer here

Correct Answer: -3

Deg^°

Rad

Multiple Select

Which is true about any midsegment in a triangle?

(Select all that apply.) #51

• The midsegment is parallel to its corresponding side.

• The midsegment is perpendicular to its corresponding side.

• The midsegment is half as long as its corresponding side.

• The midsegment connects the midpoints of two sides of a triangle.

• The midsegment is twice as long as its corresponding side.

Math Response

Find the value of x. #53

(PARALLEL SIDE)=2(MIDSEGMENT)

Type answer here

Correct Answer: 3

Deg^°

Rad