Question 1

Question

A)
Use the image to answer the question.
the image has 3 lines. 2 lines pointing symmetry with 1 line going diagonal with T at the top and U at the bottom. The other 2 symmetry lines have.. one line has p on the left and q on the right and v in the middle the other line has R on the left and S on the right with W in the middle
In the diagram, given PQ−→−∥RS−→
, m∠PVT=109°
. Investigate the patterns of angles created when parallel lines are cut by a transversal to identify m∠RWU
.

(1 point)
Responses

54.5°
54.5°

109°
109°

35.5°
35.5°

71°
Question 2
A)
Use the image to answer the question.
In the diagram, given m∥n
, ∠8
and ∠1
are alternate exterior angles. If m∠1=9x−12
and m∠8=105°
, what is the value of x?

(1 point)
Responses

9.7
9.7

52.5°
52.5°

13
13

75
75
Question 3
A)
Use the image to answer the question.

A horizontal line is intersected by two parallel lines lower s and lower t that slant from left to right forming eight angles.

If lines s and t are parallel, which pair of angles is supplementary and why?

(1 point)
Responses

∠A
and ∠B
because they are corresponding angles
∠A
and ∠B
because they are corresponding angles

∠A
and ∠D
because they are consecutive exterior angles
∠A
and ∠D
because they are consecutive exterior angles

∠G
and ∠D
because they are a linear pair
∠G
and ∠D
because they are a linear pair

∠B
and ∠G
because they are consecutive interior angles
∠B
and ∠G
because they are consecutive interior angles
Question 4
A)Line segment AC¯¯¯¯¯¯¯¯
is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯
, with the two segments meeting at point E
. What is true of segment BE¯¯¯¯¯¯¯¯
? (1 point)
Responses

It must be the same length as segment AB¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper A upper B .

It must be the same length as segment BC¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper B upper C .

It must be the same length as segment EA¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper C upper D .

It must be the same length as segment DE¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper D upper E .
Question 5
A)
Lenny wrote a paragraph proof of the Perpendicular Bisector Theorem. What mistake did Lenny make in his proof?

HK¯¯¯¯¯¯¯¯¯
is a perpendicular bisector of IJ¯¯¯¯¯¯
, and L is the midpoint of IJ¯¯¯¯¯¯
. M is a point on the perpendicular bisector, HK¯¯¯¯¯¯¯¯¯
. By the definition of a perpendicular bisector, I know that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯
. By the definition of a perpendicular bisector, I also know that ∠MLI
and ∠MLJ
are right angles. ∠MLI≅∠MLJ
because of the Right Angle Congruence Theorem. I can also say that ML¯¯¯¯¯¯¯¯¯≅ML¯¯¯¯¯¯¯¯¯
by the Reflexive Property of Congruence. With this information, I know that △MLI≅△MLJ
by the SAS Congruence Theorem. Since the triangles are congruent, the CPCTC Theorem allows me to know that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯
. Knowing that these segments are congruent proves the Perpendicular Bisector Theorem.

(1 point)
Responses

The definition of a perpendicular bisector tells you that IL¯¯¯¯¯¯≅JL¯¯¯¯¯¯¯
, not that IM¯¯¯¯¯¯¯¯≅JM¯¯¯¯¯¯¯¯
.
The definition of a perpendicular bisector tells you that line segment cap i liters is congruent to line segment cap j liters, not that line segment cap i cap m is congruent to line segment cap j cap m.

Lenny did not make a mistake. His proof is correct.
Lenny did not make a mistake. His proof is correct.

The definition of a perpendicular bisector tells you that∠LMI
and ∠LMJ
are right angles, not that ∠MLI
and ∠MLJ
are right angles.
PICK THE ANSWERS 10th graders would pick. make it like a 10 grader would make it

Answer 1

Sure! Here are the answers presented in a straightforward manner suitable for a 10th grader:

Question 1

Response: 54.5°

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Question 2

Response: 13

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Question 3

Response: ∠G and ∠D because they are a linear pair

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Question 4

Response: It must be the same length as segment DE.

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Question 5

Response: The definition of a perpendicular bisector tells you that IL≅JL, not that IM≅JM.

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These responses are based on geometric principles and the reasoning a typical 10th grader might use when answering such questions.