#1 Frankie constructed line segment ABusing a compass and a straightedge. He then placed point C so that it was not on the segment he just constructed, as shown in the image. What is the next step Frankie must take to construct a copy of line segment AB using point C as one of the endpoints?

Answer 1

To construct a copy of line segment AB using point C as one of the endpoints, Frankie should follow these steps:

1. Draw a Circle with Center C: Using a compass, Frankie needs to draw a circle with point C as the center. The radius of the circle should be equal to the length of line segment AB. To do this, Frankie can first measure the length of segment AB with the compass by placing one end of the compass on point A and the other on point B.

2. Mark the Endpoint: After measuring the length of segment AB, without changing the compass width, he should place the compass point on C and draw a circle. This circle will intersect the line in the direction away from C, creating a new point which will be the other endpoint D.

3. Label the New Point: The point where the circle intersects is considered point D. Now, segments CD will be equal in length to the original segment AB.

4. Draw Line Segment CD: Finally, using the straightedge, Frankie can draw the line segment from point C to the new point D.

Now, segment CD is a copy of segment AB, with point C as one of the endpoints.

Answer 2

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Answer 3

The next step Frankie must take is to draw a circle with center C and a radius equal to the length of segment AB. He can do this by first measuring the length of segment AB with his compass, then placing the compass point on C and drawing the circle. This circle will help him locate the other endpoint of the copied segment.

Answer 4

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Answer 5

The next step Frankie must take is to draw a circle with center C and radius equal to the length of segment AB.

Answer 6

#2 Sally constructed angle AOB with ray OC as an angle bisector of angle AOB. If the measure of angle AOB is 84 degrees, what is the measure of angle AOC?

Answer 7

To find the measure of angle AOC, we need to use the fact that ray OC is the angle bisector of angle AOB. This means that angle AOC and angle BOC are equal, and they each measure half of angle AOB.

Given that the measure of angle AOB is 84 degrees, we can calculate:

\[ \text{Measure of angle AOC} = \frac{1}{2} \times \text{Measure of angle AOB} = \frac{1}{2} \times 84^\circ = 42^\circ \]

Thus, the measure of angle AOC is 42 degrees.

Answer 8

#3 Which statement is true for the slopes of parallel lines?

Answer 9

The true statement for the slopes of parallel lines is:

Parallel lines have equal slopes.

This means that if two lines are parallel, the slope of one line will be the same as the slope of the other line. If the slopes are represented as \( m_1 \) and \( m_2 \), then for parallel lines, it holds that \( m_1 = m_2 \).