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 = $$°
Question 16
A)
Use the picture below to classify the type of angle relationship for the angles given.



(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
<13 and <2 Response area
<7 and <9 Response area
<16 and <5 Response area
<17 and <23 Response area
<10 and <13 Response area


Question 17
A)
In the diagram below, quadrilateral TURS is a rhombus. If RV = 2x+4 and VT = 8x-8, find the length of VT. You must show all steps in order to receive full credit. You may upload a picture of your work by using the icon or your may type out your work.

(3 points)
0 / 10000 Word Limit
Question 18
A)
Carlos is playing pool. He has 1 ball left to make in a pocket and then he will win. He knows that a pool table is a rectangle and there are 6 pockets that you can hit the balls into (indicated by points A, B, C, F, E, and D on the diagram below). In his head, he drew a line segment between points F and C and then pictured its perpendicular bisector, GH¯¯¯¯¯¯¯¯
. The ball he needs to hit is at point I, on the perpendicular bisector. He is trying to decide which pocket is closer, F or C.

a. Which pocket is closer?

(1 point)
Responses

They are the same distance from point I
They are the same distance from point I

Pocket C is closer to point I than Pocket F
Pocket C is closer to point I than Pocket F

Pocket F is closer to Point I than Pocket C

Answer 1

Question 1

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

Question 2

Response: Statement #1 is the best way for Krystina to determine if the lines are parallel.

Question 3

Response: Line A is perpendicular to Line B.

Question 4

Response: x = 30. (Explanation: Since PQ ∥ RS, ∠UWS and ∠QVU are consecutive interior angles which are supplementary, thus ∠UWS + ∠QVU = 180. Set up the equation: 4x - 18 + 102 = 180 and solve for x.)

Question 5

Response: Transitive Property of Equality.

Question 6

Response:

1. ∠FDP ≅ ∠EPG (because they are corresponding angles).
2. DP ¯¯¯¯¯¯¯¯≅ EP ¯¯¯¯¯¯¯¯ (because they are segments formed by the perpendicular bisector).

Question 7

Response: 120°. (Explanation: The formula for the interior angle of a regular polygon is (n-2)(180)/n. For a hexagon, n=6, so (6-2)(180)/6 = 120.)

Question 8

Response: AC = 34. (Explanation: Set BD = AC, so x + 20 = 4x + 14; solving gives x = 6, thus AC = 4(6) + 14 = 38.)

Question 9

Response: 22 (Explanation: Set up the equation (3x - 7) + (x + 15) = 180 and solve for x.)

Question 10

Response: x = 20 and y = 8.

Question 11

Response: VT ¯¯¯¯¯¯¯. (Explanation: Opposite sides of a parallelogram are congruent.)

Question 12

Response: (3, 6).

Question 13

Response: x = 3. (Explanation: Set the lengths equal: 2x + 9 = 12x - 11, solve for x.)

Question 14

Response:

• m∠ABC= 124°
• m∠AEB= 56°
• m∠ADE= 56°

Question 15

Response: b = 180°.

Question 16

Guess based on angle relationships:

• <13 and <2 --> Alternate interior angles
• <7 and <9 --> Corresponding angles
• <16 and <5 --> Alternate exterior angles
• <17 and <23 --> Same-side interior angles
• <10 and <13 --> Vertical angles

Question 17

Response:

1. Set the equations equal: 2x + 4 = 8x - 8.
2. Solve for x:
   • 10 = 6x
   • x = 5.
3. Substitute x back to find VT: VT = 8(5) - 8 = 32.

Question 18

Response: They are the same distance from point I. (Explanation: Point I lies on the perpendicular bisector of segment FC, so it is equidistant from points F and C.)