Question

geometry chapter 1 review

1. consider the diagram shown below.

which of the following statements best describes the construction in the diagram?
a. ab < cd
b. \\(\overline{ab}\cong\overline{cd}\\)
c. points, a, b, and d are collinear.
d. points, a, c, and d are collinear.

1. which construction is best represented by the steps illustrated below?

step i
step ii
step iii
step iv
a. perpendicular bisector of a line segment.
b. angle bisector
c. congruent angle
d. congruent segment

1. which of the following statements is not a correct step of constructing segment cd congruent to segment ab.

i. using a straightedge, draw a reference line. draw a dot on the reference line to mark your starting point for the construction. label the point c.
ii. open your compass so that the anchor is on one endpoint of line segment ab and the pencil point is beyond the other endpoint.
iii. without changing the compass opening, place the anchor on point c on your reference line segment. make a mark that crosses this line segment.
iv. label the point where the mark crosses the line segment with the letter d.
a. i
b. ii
c. iii
d. iv

Explanation:

Step1: Analyze question 1

The diagram shows constructing a segment CD congruent to AB. Collinearity of points is not shown as relevant here. So $\overline{AB}\cong\overline{CD}$ is the best - description.

Step2: Analyze question 2

The steps show opening the compass to the length of segment AB and then transferring that length to another line to create segment CD. This is constructing a congruent segment.

Step3: Analyze question 3

All steps I, III, and IV are correct for constructing a congruent segment. Step II is incorrect as the compass should be opened to the length of segment AB with the anchor on one endpoint of AB and the pencil point on the other endpoint, not beyond.

Answer:

1. B. $\overline{AB}\cong\overline{CD}$
2. D. congruent segment
3. B. II