A)

Question

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)

Answer 1

The statement "A trapezoid is a four-sided figure with one set of parallel lines" is a definition. Therefore, you should enter 2.

Answer 2

Thuy examines the figure in the image. She needs to determine if is a copy of . What
must she do to show that is a constructed copy of ?
(1 point)
NO
¯¯¯¯¯¯¯¯ PQ
¯¯¯¯¯¯¯¯
NO
¯¯¯¯¯¯¯¯ PQ
¯¯¯¯¯¯¯¯
She must measure the distance from point to point using a compass and place the
compass on point to see if point is the same distance.
O Q
P N
She must measure the distance from point to point using a compass and place the
compass on point to see if point is the same distance.
M Q
M O
She must measure the distance from point to point using a compass and place the
compass on point to see if point is the same distance.
M N
P M
She must measure the distance from point to point using a compass and place the
compass on point to see if point is the same distance.

Answer 3

To show that the figure \( NO \) is a constructed copy of the figure \( PQ \), Thuy must compare the lengths of the corresponding segments. Since she needs to confirm whether the corresponding points on both figures are the same distance apart, the best option would involve measuring the distances between the pairs of corresponding points.

However, your provided options seem a bit jumbled, but based on what you're trying to determine, the correct procedure should be measuring the distance from each point in one figure to corresponding points in another and ensuring those measurements are equal.

Thus, it seems like an appropriate option could be similar to:

"She must measure the distance from point \( P \) to point \( Q \) using a compass and place the compass on point \( M \) to see if point \( N \) is the same distance."

Make sure to choose the answer that mentions measuring corresponding points to confirm they are the same distance apart.

Answer 4

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

Answer 5

To determine the segment that is the segment bisector in Lexi's scenario, we need to focus on the context provided about folding the paper and creating point \( R \) at the intersection of the fold and the line segment \( CD \). A segment bisector is defined as a line, ray, or segment that divides another segment into two equal parts.

In this case, the fold suggests that \( R \) is equidistant from points \( C \) and \( D \), meaning \( CR \) is equal to \( DR \).

Thus, the segment bisector in this scenario would be:

\( CR \) ⟶ or \( DR \) ⟶.

This means the correct option would include the line or segment that passes through point \( R \) and is perpendicular to line segment \( CD \), dividing it into two equal parts.

Since the options provided are a bit unclear, the segment you’re looking for is likely the one that runs through point \( R \) and intersects \( CD \) at the midpoint:

So choose the line segment that represents this bisector, most likely just \( QR \) ⟶ if it connects to point \( R \) and is indeed a bisector for \( CD \).

Answer 6

A) Carlos constructed the angle bisector of by constructing ray . Carlos then
constructed the angle bisector of by constructing ray . If the measurement of
is 56 degrees, what is the measurement of ? (1 point)
∠JKI KM
∠MKI KN
∠JKI ∠NKI
The measurement of ∠NKI is 112 degrees.
The measurement of ∠NKI is 28 degrees.
The measurement of ∠NKI is 7 degrees.
The measurement of ∠NKI is 14 degrees.

Answer 7

To determine the measurement of \( \angle NKI \), we will analyze what has been provided:

1. Carlos constructed the angle bisector of \( \angle JKI \) creating ray \( KM \), which means that \( KM \) divides \( \angle JKI \) into two equal angles. Since the measure of \( \angle JKI \) is \( 56 \) degrees, each of the angles formed is half of this measure: \[ \angle JKM = \angle MKI = \frac{56}{2} = 28 \text{ degrees} \]

2. Then, Carlos constructed the angle bisector of \( \angle MKI \) creating ray \( KN \). Since \( \angle MKI \) is \( 28 \) degrees, \( KN \) will divide this angle into two equal parts as well: \[ \angle NKI = \frac{28}{2} = 14 \text{ degrees} \]

Thus, the measurement of \( \angle NKI \) is \( 14 \) degrees.

The correct answer is: The measurement of \( \angle NKI \) is 14 degrees.