# 1. Two horizontal lines are shown. The top one is a dashed line. A diagonal line passes through both of them and points are drawn where the diagonal lines intersects the two lines. Compass arcs are shown around the top right corresponding angles. Two arcs are drawn around each angle, intersecting on the horizontal lines.

Which of the following is being constructed in the image?

A. a line parallel to a given line through a point not on the line
B. a line perpendicular to a given line through a point not on the line
C. a line segment that is congruent to a given line segment
D. a perpendicular bisector of a line segment

## To determine which construction is being shown in the image, let's examine the given options one by one:

A. Constructing a line parallel to a given line through a point not on the line: This construction involves drawing a line parallel to a given line, but through a point not on that line. However, in the image, there is no point mentioned that is not on the given line. Therefore, this option can be eliminated.

B. Constructing a line perpendicular to a given line through a point not on the line: Similar to option A, this construction also involves drawing a line perpendicular to a given line through a point not on the line. Again, in the image, there is no point mentioned that is not on the given lines. So, this option can also be eliminated.

C. Constructing a line segment that is congruent to a given line segment: This construction involves creating a line segment that has the same length as a given line segment. However, in the image, no lines or line segments are being measured or compared for their lengths. Thus, this option can be eliminated.

D. Constructing a perpendicular bisector of a line segment: This construction involves drawing a line that intersects a given line segment at a 90-degree angle and bisects (cuts in half) the line segment into two equal parts. In the image, the diagonal line passes through both horizontal lines and intersects them at right angles, creating equal angles on either side of the intersection. This is characteristic of a perpendicular bisector. Thus, the correct answer is option D.

In summary, the construction being shown in the image is the construction of a perpendicular bisector of a line segment, making the correct answer D.

## Hmm, let me think about this in a funny way. Well, it seems like the image is trying to make some geometry magic happen. Let's see...

Ah, I got it! It's like the lines are having a dance party, with the diagonal line cutting through them and creating some wild angles. And those compass arcs? They are like the DJ playing some funky tunes around those angles, jazzing them up.

So, based on this fabulous dance party scenario, I'd say we're constructing... *drumroll* ... A. a line parallel to a given line through a point not on the line! It's like we're trying to find that dance partner who moves in perfect sync, but never actually touches the other line. How groovy is that?

## Based on the provided description, the image is showing the construction of a line parallel to a given line through a point not on the line.

The presence of the diagonal line passing through both lines and intersecting them at points indicates the construction of a parallel line. The compass arcs drawn around the top right corresponding angles suggest that the angles formed by the intersection of the diagonal line with the horizontal lines are equal, which is a characteristic of parallel lines. Hence, the correct answer is A. a line parallel to a given line through a point not on the line.

## 1. A

2. A
3. A
4. B
5. C
6. B
7. A
8. D
(on your own for the rest of them)

11. B is incorrect; because (4x-2) and (3x+6) are alternate interior angles.
(4x-2)= (3x+6)
4x-2= 3x+6
4x-3x=6+2

12. 1. 63*+36*+x*= 180* 2. x+z+180* 3. 13*+z*=y*=180*
99*+x*+180* 81*+z=180 13*+99*+y*=180*
x*=180*-99* z=180*-81* 112*+y*=180*
<x= 81 z=99 y*=180*-112*
y*=68*

x=8