Question 1

Question

A)Stephen is trying to find the slope of a line that goes through the coordinates (8,-6) and (0,8) using the formula ΔyΔx=y2−y1x2−x1
. Stephen says the slope should be calculated as 0−88−(−6) = −47
. Is his calculation for slope correct? If not, why?(1 point)
Responses

Stephen is correct.
Stephen is correct.

Stephen is incorrect because he calculated the change in x over the change in y.
Stephen is incorrect because he calculated the change in x over the change in y.

Stephen is incorrect because he added instead of subtracted.
Stephen is incorrect because he added instead of subtracted.

Stephen is incorrect because he didn't simplify correctly.
Stephen is incorrect because he didn't simplify correctly.
Question 2
A)
Krystina is trying to see if two lines are parallel. The equations of the lines are

y=23x+7

y=23x−5

Pick the number of the statement that best describes how she should determine if they are parallel.

Statement #1: Krystina should verify that the lines have the same slope but different y- intercepts.

Statement #2: Krystina should verify that the lines have the same y-intercept but different slopes.

(1 point)
Statement # $$ is the best way for Krystina to determine if the lines are parallel
Question 3
A)
Given the table below, which of the following statements is true?

Line Equation
Line A y=−12x−2
Line B y=2x−3
Line C y=12x+2
Line D y=2x+5



(1 point)
Responses

Line B is perpendicular to Line D
Line B is perpendicular to Line D

Line A is perpendicular to Line B
Line A is perpendicular to Line B

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line C is perpendicular to Line D
Line C is perpendicular to Line D
Question 4
A)
In the diagram below, PQ∥RS
. If ∠UWS = 4x−18
and ∠QVU = 102°
, what is the value of x?

(1 point)
x=
$$
Question 5
A)
Which of the following statements correctly completes the proof that consecutive interior angles are supplementary?

Given: n∥m

Statements Reasons
1. m∡A+m∡C=180°
1. Linear Pairs are supplementary
2. m∡A=m∡E
2. __________________________
3.. m∡E+m∡C=180°
3. Substitution
4. ∠E and ∠C
are supplementary 4. Definition of Supplementary Angles


(1 point)
Responses

Corresponding Angles Postulate
Corresponding Angles Postulate

Definition of congruence
Definition of congruence

Transitive Property of Equality
Transitive Property of Equality

Vertical Angles Theorem
Vertical Angles Theorem
Question 6
A)ED¯¯¯¯¯¯¯¯
is a perpendicular bisector of GF¯¯¯¯¯¯¯¯
, and they intersect at point P. Which of the following statements must be true? Select the TWO answers that are correct.(1 point)
Responses

∠FDP≅∠EPG
∠FDP≅∠EPG

∠DPF≅∠DPG
∠DPF≅∠DPG

DP¯¯¯¯¯¯¯¯≅EP¯¯¯¯¯¯¯¯
line segment cap d cap p is congruent to line segment cap e cap p

GF¯¯¯¯¯¯¯¯≅ED¯¯¯¯¯¯¯¯
line segment cap g cap f is congruent to line segment cap e cap d

GP¯¯¯¯¯¯¯¯≅FP¯¯¯¯¯¯¯¯
line segment cap g cap p is congruent to line segment cap f cap p
Question 7
A)Marco is drawing a regular hexagon. He needs to know what the measure is of one interior angle. (1 point)
What is the measure of one interior angle? $$°
Question 8
A)
The figure below is a rectangle. If BD = x+20 and AC = 4x+14, what is the total length of AC?

(1 point)
AC =
$$
Question 9
A)
The interior angle of point B measures (3x-7) degrees and the interior angle of point D measures (x+15) degrees. What is the value of angle D?

(1 point)
Responses

43
43

11
11

22
22

26
26
Question 10
A)Ema drew quadrilateral ABCD. If side AB = 40y, side BC = 4+3x, side CD = 8y+32, and side AD = 9x-20, for what values of x and y can Ema be sure that her quadrilateral is a parallelogram?(1 point)
Responses

x = 40 and y = 16
x = 40 and y = 16

x = 20 and y = 8
x = 20 and y = 8

x = 4 and y = 1
x = 4 and y = 1

x = 1 and y = 4
x = 1 and y = 4
Question 11
A)

If quadrilateral VSTU is a parallelogram, which segment of the figure must be congruent to VE¯¯¯¯¯¯¯¯
?

(1 point)
Responses

SE¯¯¯¯¯¯¯
line segment cap s cap e

VT¯¯¯¯¯¯¯
line segment cap v cap t

VS¯¯¯¯¯¯¯
line segment cap v cap s

ET¯¯¯¯¯¯¯
line segment cap e cap t
Question 12
A)
When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?

(1 point)
Responses

(13 ,13)
(13 ,13)

(3,6)
(3,6)

(3, 143
)
(3, 14 thirds)

(3,5)
(3,5)

(103 , 133)
(103 , 133)
Question 13
A)

Given rectangle BCDA as shown, find the value of x if BE = 2x+9 and EC = 12x-11

(1 point)
x=
$$
Question 14
A)

In the diagram above, quadrilateral ABCD is a rhombus. If the m∠DAB
= 124°
find the measurements below.

(3 points)
m∠ABC=
$$ °

m∠AEB=
$$ °

m∠ADE=
$$ °

Question 15
A)(1 point)
<b = $$°

Answer 1

Let's answer each of the questions one by one:

Question 1

Stephen is incorrect because he added instead of subtracted. To find the slope using the formula \( \Delta y / \Delta x = (y_2 - y_1) / (x_2 - x_1) \), Stephen should be using:

• \( y_2 = 8 \) and \( y_1 = -6 \)
• \( x_2 = 0 \) and \( x_1 = 8 \)

The correct calculation should be: \[ \text{slope} = \frac{8 - (-6)}{0 - 8} = \frac{8 + 6}{0 - 8} = \frac{14}{-8} = -\frac{7}{4} \]

Question 2

Statement #1 is the best way for Krystina to determine if the lines are parallel. Two lines are parallel if they have the same slope and different y-intercepts.

Question 3

Line A is perpendicular to Line C. Line A has a slope of -1/2, while Line C has a slope of 1/2. Slopes that multiply to -1 are perpendicular.

Question 4

To solve for x, we know that \( \angle UWS \) and \( \angle QVU \) are alternate interior angles formed by parallel lines \( PQ \parallel RS \): Given: \( \angle UWS = 4x - 18 \) and \( \angle QVU = 102^\circ \).

So, we set them equal: \[ 4x - 18 = 102 \] Adding 18 to both sides gives: \[ 4x = 120 \] \[ x = 30 \] Thus, \( x = 30 \).

Question 5

Transitive Property of Equality. The transitive property allows you to substitute equal angles in place of one another.

Question 6

Correct statements:

• \( \angle FDP \cong \angle EPG \) (because they are corresponding angles since ED is a perpendicular bisector of GF)
• \( DP \cong EP \) (because ED is a perpendicular bisector).

Question 7

To find the measure of one interior angle of a regular hexagon, use the formula: \[ \text{Interior angle} = \frac{(n-2) \times 180}{n} \] Where \( n = 6 \) for a hexagon: \[ \frac{(6 - 2) \times 180}{6} = \frac{720}{6} = 120° \] So the measure of one interior angle is 120°.

Question 8

Given \( BD = x + 20 \) and \( AC = 4x + 14 \) in a rectangle \( ABCD \), we know \( AC = BD \). Thus: \[ 4x + 14 = x + 20 \] Solving for \( x \): \[ 4x - x = 20 - 14 \implies 3x = 6 \implies x = 2 \] Now substitute \( x \) back into \( AC \): \[ AC = 4(2) + 14 = 8 + 14 = 22 \] So, AC = 22.

Question 9

Given angles measure \( (3x-7) \) and \( (x+15) \): Assuming they are supplementary: \[ (3x - 7) + (x + 15) = 180 \] Simplifying this: \[ 4x + 8 = 180 \implies 4x = 172 \implies x = 43 \] Thus \( \angle D = x + 15 = 43 + 15 = 58 \).

Question 10

To find when Ema's quadrilateral ABCD is a parallelogram, we equate opposite sides:

1. \( 40y = 8y + 32 \) leads to \( 32y = 32 \implies y = 16 \).
2. \( 4 + 3x = 9x - 20 \) leads to \( 3x - 9x = -20 - 4 \implies -6x = -24 \implies x = 4 \).

So the values are x = 4 and y = 16.

Question 11

SE is congruent to VE. In any parallelogram, opposite sides or segments are congruent.

Question 12

The centroids of triangles are calculated using the averages of the vertices. Assuming the triangles vertices are provided and averaging \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \): This requires coordinates for the precise answer.

Question 13

Given \( BE = 2x+9 \) and \( EC = 12x-11 \) with \( BE = EC \): \[ 2x + 9 = 12x - 11 \] \[ 9 + 11 = 12x - 2x \implies 20 = 10x \implies x = 2 \]

Question 14

Using \( \angle DAB = 124° \):

• \( m∠ABC = \text{same as } DAB = 124° \)
• \( m∠AEB = 180° - 124° = 56° \)
• \( m∠ADE = 124° \), angles opposite in rhombus are equal.

Question 15

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