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A)

Use the image to answer the question.

Diagonal lines u and t intersect at a right angle. Line t slopes upward to the right, and line u slopes downward to the right.

What is the precise definition of the figure in the image?

(1 point)
Responses

a part of the circumference of a circle or other curve that measures the distance between two points on a curve
a part of the circumference of a circle or other curve that measures the distance between two points on a curve

a line that intersects another line at a 90-degree angle
a line that intersects another line at a 90-degree angle

a straight figure that has no thickness and extends infinitely in two opposite directions
a straight figure that has no thickness and extends infinitely in two opposite directions

a straight line that always remains the same distance from another line and, therefore, never intersects it
a straight line that always remains the same distance from another line and, therefore, never intersects it
Question 2
A)
Consider the following statement:

A trapezoid is a four-sided figure with one set of parallel lines.

Enter 1 if the statement is a conjecture.

Enter 2 if the statement is a definition.

Enter 3 if the statement is a theorem.

(1 point)
$$
Question 3
A)
Use the image to answer the question.

Two line segments extend from point upper M. One slopes upward to the right. One slopes downward. The segments intersect the left side of a circle and terminate on the right side of the circle.

Thuy examines the figure in the image. She needs to determine if NO¯¯¯¯¯¯¯¯ is a copy of PQ¯¯¯¯¯¯¯¯. What must she do to show that NO¯¯¯¯¯¯¯¯ is a constructed copy of PQ¯¯¯¯¯¯¯¯?

(1 point)
Responses

She must measure the distance from point N to point O using a compass and place the compass on point P to see if point Q is the same distance.
She must measure the distance from point upper N to point upper O using a compass and place the compass on point upper P to see if point upper Q is the same distance.

She must measure the distance from point M to point Q using a compass and place the compass on point M to see if point O is the same distance.
She must measure the distance from point upper M to point upper Q using a compass and place the compass on point upper M to see if point upper O is the same distance.

She must measure the distance from point O to point Q using a compass and place the compass on point P to see if point N is the same distance.
She must measure the distance from point upper O to point upper Q using a compass and place the compass on point upper P to see if point upper N is the same distance.

She must measure the distance from point M to point N using a compass and place the compass on point P to see if point M is the same distance.
She must measure the distance from point upper M to point upper N using a compass and place the compass on point upper P to see if point upper M is the same distance.
Question 4
A)
Use the image to answer the question.

A scalene triangle with its base oriented nearly vertical is formed by the intersection of two lines and a line segment. A third line slopes upward from left to right and passes through the base of the triangle and its apex.

Lexi started with CD¯¯¯¯¯¯¯¯ on her paper. She folded her paper so that point C was on top of point D. Then, she unfolded her paper and labeled the intersection of the fold and the line segment with point E.​ She used a straight edge to draw QR←→ at an arbitrary angle through point E. Finally, she drew CR←→ through points C and R and DR←→ through points D and R. Which line segment or line is the segment bisector in this scenario?

(1 point)
Responses

QR←→
Modifying above upper Q upper R with two-way arrow

CR←→
Modifying above upper C upper R with two-way arrow

CD¯¯¯¯¯¯¯¯
Modifying above upper C upper D with bar

DR←→
Modifying above upper D upper R with two-way arrow
Question 5
A)
Use the image to answer the question.

An illustration shows angle Q A L. Ray A B P Q and ray A C L extend from vertex A. An arc intersects both rays, connecting B and C. Another arc intersects Q.

What is the construction that needs to be done to make a copy of ∠BAC?

(1 point)
Responses

Using a compass, measure the distance from point Q to point B. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.
Using a compass, measure the distance from point upper Q to point upper B . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P .

Using a compass, measure the length from point B to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.
Using a compass, measure the length from point upper B to point upper C . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P .

Using a compass, measure the length from point A to point C. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.
Using a compass, measure the length from point upper A to point upper C . Then, make another arc by placing the pointed end of the compass on point upper Q and draw a small arc that intersects with the larger arc above point upper P .

Using a straight edge, construct a horizontal line from point P that intersects with the arc to find the middle of the angle.
Using a straight edge, construct a horizontal line from point upper P that intersects with the arc to find the middle of the angle.
Question 6
A)Carlos constructed the angle bisector of ∠JKI by constructing ray KM. Carlos then constructed the angle bisector of ∠MKI by constructing ray KN. If the measurement of ∠JKI is 56 degrees, what is the measurement of ∠NKI?(1 point)
Responses

The measurement of ∠NKI is 112 degrees.
The measurement of angle upper N upper K upper I is 112 degrees.

The measurement of ∠NKI is 14 degrees.
The measurement of angle upper N upper K upper I is 14 degrees.

The measurement of ∠NKI is 28 degrees.
The measurement of angle upper N upper K upper I is 28 degrees.

The measurement of ∠NKI is 7 degrees.
The measurement of angle upper N upper K upper I is 7 degrees.
Question 7
A)Identify the diagram that shows the first step in the construction of a perpendicular bisector.(1 point)
Responses

A line segment has 2 end points, A and B. Two arcs, one open to the left and one to the right, are bisected by the line segment A B to the right of its center and left of its center, respectively.
Image with alt text: A line segment has 2 end points, A and B. Two arcs, one open to the left and one to the right, are bisected by the line segment A B to the right of its center and left of its center, respectively.

Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.
Image with alt text: Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.

A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.
Image with alt text: A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.

A straight line segment with end points A and B is shown. The left end point is A, and the right end point is B.
Image with alt text: A straight line segment with end points A and B is shown. The left end point is A, and the right end point is B.
Question 8
A)
Use the images to answer the question.

Step 1: A horizontal line segment is drawn, with the endpoints labeled upper L and upper D, left to right. A pencil is shown above segment upper L upper D with its tip pointed towards the left of point upper D.
Step 2: A horizontal line segment upper L upper D is drawn left to right. A left-to-right slanted line intersects segment upper L upper D at point upper E. Point upper U is labeled on the line above and between upper L and upper D.
Step 3: Horizontal line segment upper L upper D is drawn left to right. A left-to-right slanted line intersects segment upper L upper D at point upper E and extends indefinitely in either direction.
Step 4: Horizontal line segment upper L upper D is drawn left to right. A left-to-right slanted line intersects segment upper L upper D at point upper E and extends indefinitely in either direction. Two arcs are drawn.
Determine the type of construction being done from the steps shown.

(1 point)
Responses

angle bisector
angle bisector

perpendicular bisector
perpendicular bisector

parallel lines through a point not on the given line
parallel lines through a point not on the given line

perpendicular lines
perpendicular lines
Question 9
A)Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)
Responses

9, 17, 11
9, 17, 11

18, 10, 8
18, 10, 8

18, 11, 8
18, 11, 8

11, 19, 9
11, 19, 9
Question 10
A)
Use the image to answer the question.

An inverted triangle shows the upper left vertex labeled as house, with a side marked 5 miles leading to the lower right vertex labeled as farmer's market. The third vertex at the bottom is labeled bank.

The diagram shows the distance between your house, the bank, and the farmer’s market. You need to stop at the bank before going to the farmer’s market. Given the information in the diagram, identify which statement is true.

(1 point)
Responses

The distance from your house to the bank and then the farmer’s market is greater than 5 miles.
The distance from your house to the bank and then the farmer’s market is greater than 5 miles.

The distance from your house to the bank and then the farmer’s market is less than 5 miles.
The distance from your house to the bank and then the farmer’s market is less than 5 miles.

The distance from your house to the bank and then the farmer’s market is equal to 5 miles.
The distance from your house to the bank and then the farmer’s market is equal to 5 miles.

The distance from your house to the bank and then the farmer’s market is 8 miles.
The distance from your house to the bank and then the farmer’s market is 8 miles.

1 answer

Here are the answers to your questions based on the descriptions you provided:

Question 1:
The precise definition of the figure in the image (diagonal lines u and t intersecting at a right angle): Response: a line that intersects another line at a 90-degree angle.

Question 2:
Consider whether the statement "A trapezoid is a four-sided figure with one set of parallel lines" is a conjecture, definition, or theorem. Response: 2 (this is a definition).

Question 3:
To show that NO is a constructed copy of PQ, what must Thuy do? Response: She must measure the distance from point N to point O using a compass and place the compass on point P to see if point Q is the same distance.

Question 4:
Which segment or line is the segment bisector in Lexi's scenario? Response: CD (the segment CD is being bisected).

Question 5:
What construction needs to be done to make a copy of ∠BAC? Response: Using a compass, measure the distance from point Q to point B. Then, make another arc by placing the pointed end of the compass on point Q and draw a small arc that intersects with the larger arc above point P.

Question 6:
What is the measurement of ∠NKI if ∠JKI is 56 degrees? Response: The measurement of ∠NKI is 28 degrees.

Question 7:
Identify the diagram that shows the first step in the construction of a perpendicular bisector. Response: A line segment has 2 end points, A and B. Two arcs, one open to the left and one to the right, are bisected by the line segment A B to the right of its center and left of its center, respectively.

Question 8:
Determine the type of construction being done from the steps shown. Response: perpendicular bisector.

Question 9:
Which set of side lengths does not form a triangle? Response: 18, 10, 8 (use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side).

Question 10:
Identify which statement is true regarding the distances in the triangle. Response: The distance from your house to the bank and then the farmer’s market is greater than 5 miles.

If you have further questions or need clarifications, feel free to ask!