Geometry Basics Unit Test 5 of 155 of 15 Items Question Use the image to answer the question. What is the construction that needs to be done to make a copy of ∠BAC ? (1 point) Responses 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. 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 .

Answer 1

To make a copy of ∠BAC, you want to replicate the angle at a new point (point Q) using a compass and straightedge. The correct construction process would be:

1. Use a compass to measure the length from point B to point C.
2. With the pointed end of the compass at point Q, draw an arc that intersects the new line created above point P.

This implies that the correct choice should be:

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.

This process ensures that you accurately copy the angle from the original point to the new location.

Answer 2

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 14 degrees. The measurement of angle upper N upper K upper I is 14 degrees. The measurement of ∠NKI is 7 degrees. The measurement of angle upper N upper K upper I is 7 degrees. 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 28 degrees.

Answer 3

To find the measurement of ∠NKI given that ∠JKI is 56 degrees, we need to follow the steps of angle bisectors:

1. Carlos constructed ray KM to bisect ∠JKI.

   • Since ∠JKI is 56 degrees, the measure of each of the angles formed by the bisector (∠JKM and ∠MKI) is: \[ \frac{56}{2} = 28 \text{ degrees.} \]
   • So, ∠JKM = 28 degrees and ∠MKI = 28 degrees.

2. Carlos then constructed ray KN to bisect ∠MKI.

   • Now that we know ∠MKI is 28 degrees, when ray KN bisects ∠MKI, each of the angles ∠MKN and ∠NKI will measure: \[ \frac{28}{2} = 14 \text{ degrees.} \]

Thus, the measurement of ∠NKI is 14 degrees.

Therefore, the correct response is:

• The measurement of angle NKI is 14 degrees.

Answer 4

Identify the diagram that shows the first step in the construction of a perpendicular bisector.(1 point) Responses 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. 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. 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.

Answer 5

The first step in the construction of a perpendicular bisector involves placing the compass on one endpoint of the segment and drawing arcs that intersect above and below the segment. The construction typically begins by choosing a segment (let’s say AB) and then using a compass to draw two arcs of equal radius from each endpoint (A and B), so that the arcs intersect above and below the segment.

Based on your descriptions, the correct image showing the first step in the construction of a perpendicular bisector is:

The image with alt text: A line segment has 2 endpoints, 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.

This depiction reflects the initial step of drawing two arcs from points A and B, which will eventually help in finding the perpendicular bisector.

Answer 6

Geometry Basics Unit Test 8 of 158 of 15 Items Question Use the images to answer the question. Step 1: Step 2: Step 3: Step 4: Determine the type of construction being done from the steps shown. (1 point) Responses perpendicular lines perpendicular lines parallel lines through a point not on the given line parallel lines through a point not on the given line angle bisector angle bisector perpendicular bisector

Answer 7

Based on the context of your question and the typical geometry constructions, here’s how to determine the type of construction being described by the steps:

1. Perpendicular Lines - This involves creating two lines that intersect at a right angle (90 degrees).

2. Parallel Lines Through a Point Not on the Given Line - This refers to constructing lines that are parallel to an existing line but originating from a point that is not on that line.

3. Angle Bisector - This involves splitting an angle into two equal smaller angles.

4. Perpendicular Bisector - This construction creates a line that is perpendicular to a segment at its midpoint, dividing it into two equal segments.

Without seeing the actual images of Steps 1 to 4, it's challenging to specify exactly which construction is being described. However, if the steps involve creating lines that are parallel to another line from a point not on that line, then the response would be:

Parallel lines through a point not on the given line.

If the steps involved creating perpendicular relationships or dividing angles, then you would choose the appropriate response accordingly.

Please provide the visible details for each step if available, to give a more accurate identification of the construction type.