A)

Question

Lucia constructed as a copy of using a straightedge and compass. What can Lucia
say about and ?
(1 point)
CD
¯¯¯¯¯¯¯¯ AB
¯¯¯¯¯¯¯¯
AB CD
AB = CD.
1
4
AB = 2CD.
AB = CD.
1
2
AB = CD

Answer 1

Based on the information provided, it seems that Lucia constructed two segments \(AB\) and \(CD\) using a straightedge and compass, which typically suggests that these segments are created in a geometric context where they may be equal or have a specific ratio based on a construction.

Given the options regarding the relationship between \(AB\) and \(CD\):

1. \(AB = CD\)
2. \(AB = 2CD\)
3. \(AB = \frac{1}{2}CD\)

Without more specific information about the construction or the relationship intended in this problem, it is reasonable to conclude that:

• If Lucia constructed \(AB\) and \(CD\) to be equal, then \(AB = CD\).
• If she was asked to create two segments such that one is twice the length of the other, then \(AB = 2CD\).
• Conversely, if one segment is half the length of the other, then \(AB = \frac{1}{2}CD\).

If Lucia simply copied one segment using a straightedge and compass, the most likely answer is that \(AB = CD\), because copying directly indicates equality.

Thus, if asked what can be said about \(AB\) and \(CD\) under the assumption that \(AB\) was constructed to be a copy of \(CD\), the answer would be:

AB = CD.

Answer 2

Wei constructed as a copy of , as shown in the image. What was the last step that
Wei did to complete his construction?
(1 point)
CD
¯¯¯¯¯¯¯¯ AB
¯¯¯¯¯¯¯¯
Using a straightedge, he constructed a line from point A to point B.
Using a compass, he measured the length from point A to point B.
Using a straightedge, he constructed a line from point C to point D.
Using a compass, he measured the length from point C to point D.

Answer 3

In the context of geometric constructions using a straightedge and compass, if Wei constructed \(AB\) as a copy of \(CD\), he most likely followed a series of steps to ensure that \(AB\) is exactly the same length as \(CD\).

Typically, the last step in such a construction would involve ensuring the correct placement and drawing of the segment that is the copy. Here are the statements evaluated:

1. Using a straightedge, he constructed a line from point A to point B.

   • This statement indicates creating the line segment, which is a final step.

2. Using a compass, he measured the length from point A to point B.

   • Measuring the length after already having constructed \(AB\) wouldn’t make sense as the segment would already be constructed.

3. Using a straightedge, he constructed a line from point C to point D.

   • This describes the previous step of drawing the original segment and does not complete the copy.

4. Using a compass, he measured the length from point C to point D.

   • This is an essential step to determine the length, but it is not the final step in the construction process.

Since the goal of copying segment \(CD\) to create segment \(AB\) typically includes the last step where the straightedge is used to finalize the placement of the segment \(AB\), the most fitting answer is:

Using a straightedge, he constructed a line from point A to point B.

Answer 4

Nozomi constructed a copy of by using point as an endpoint of the copy of and
placing point , as seen in the image. If the measure of is 22.3 millimeters, what is the
measure of ?
(1 point)
AB
¯¯¯¯¯¯¯¯ B AB
¯¯¯¯¯¯¯¯
C AB
¯¯¯¯¯¯¯¯
AC
¯¯¯¯¯¯¯¯
The measure of AC is 44.6 millimeters. ¯¯¯¯¯¯¯¯
The measure of AC is 22.3 millimeters. ¯¯¯¯¯¯¯¯
The measure of AC is 11.15 millimeters. ¯¯¯¯¯¯¯¯
The measure of AC is 66.9 millimeters.

Answer 5

In the context of constructing a copy of segment \(AB\) using endpoint \(C\), it seems Nozomi has followed a geometric construction involving a straightedge and compass, placing point \(C\) as one endpoint of the copy of \(AB\).

Given the information provided:

• The original segment \(AB\) has a measure of 22.3 millimeters.

If Nozomi constructed segment \(AC\) as a copy of \(AB\), then segment \(AC\) would also measure the same length as \(AB\) due to the properties of copying:

• Therefore, the measure of \(AC\) would also be 22.3 millimeters.

The options given were:

1. The measure of \(AC\) is 44.6 millimeters.
2. The measure of \(AC\) is 22.3 millimeters.
3. The measure of \(AC\) is 11.15 millimeters.
4. The measure of \(AC\) is 66.9 millimeters.

Since \(AC\) is a copy of \(AB\), the correct answer is:

The measure of AC is 22.3 millimeters.

Answer 6

Aleph constructed , a line segment bisector of . How does point relate to ? If
units, what is ?
(1 point)
ZR
−−→
XY
¯¯¯¯¯¯¯¯ Z XY
¯¯¯¯¯¯¯¯
XY = 22 ZY
Point Z is the center point of XY . units. ¯¯¯¯¯¯¯¯ ZY = 11
Point Z is the midpoint of XY . units. ¯¯¯¯¯¯¯¯ ZY = 22
Point Z is the center point of XY . units ¯¯¯¯¯¯¯¯ ZY = 22
Point Z is the midpoint of XY . units. ¯¯¯¯¯¯¯¯ ZY = 11

Answer 7

If Aleph constructed a line segment bisector of segment \(XY\), it implies that point \(Z\) is located at the midpoint of segment \(XY\). This means that point \(Z\) divides segment \(XY\) into two equal parts.

Given the information that \(XY = 22\) units, if \(Z\) is the midpoint, then the lengths of segments \(XZ\) and \(ZY\) will be equal, each being half the length of \(XY\):

\[ ZY = ZY = \frac{XY}{2} = \frac{22}{2} = 11 \text{ units} \]

Based on this understanding, the correct relation and measurements are:

• Point Z is the midpoint of XY.
• ZY = 11 units.

Thus, the accurate option is:

Point Z is the midpoint of XY. units. ZY = 11

Answer 8

A)
Andy was given a line segment. He constructed a line segment bisector of the line segment
using the paper folding method. He was told that the line segment bisector divided his line
segment into pieces that are each 2.9 centimeters long. How long was Andy’s original line
segment?
(1 point)
2 cm
2.9 cm
5.8 cm
1.45 cm

Answer 9

If Andy constructed a line segment bisector that divided his original line segment into two equal pieces, and each piece measures 2.9 centimeters, we can find the length of the original line segment by adding these two equal lengths together:

\[ \text{Length of original segment} = \text{Piece length} + \text{Piece length} = 2.9 \text{ cm} + 2.9 \text{ cm} = 5.8 \text{ cm} \]

Therefore, the length of Andy’s original line segment is:

5.8 cm.