If necessary, review

**Compass and Straight Edge Practice Test**

**Practice**

**Directions**: A good score is eight correct.

1. Examine Fig. 5-12E. Based only on the information shown in this drawing, which of the following statements can we be certain is true?

(a) Quadrilateral *PSRQ* is a parallelogram but not a rectangle

(b) Quadrilateral *PSRQ* is a rhombus but not a parallelogram

(c) Quadrilateral *PSRQ* is a rectangle

(d) We can't be certain of any of the above

2. The most obvious way to “quadrisect” a large angle (that is, to divide it into four angles of equal measure) is to

(a) bisect the large angle using two different construction schemes, and then bisect the resulting angle

(b) bisect the large angle, and then bisect each of the smaller angles resulting from the bisection

(c) construct a line segment connecting the rays defining the large angle, bisect the line segment, bisect each of the smaller line segments resulting, and then construct rays from the angle apex through each point generated by the bisections

(d) give up, because there is no way to “quadrisect” an angle

3. A large angle can be “trisected” (divided into three angles of equal measure) by

(a) drawing an arc centered at the angle vertex, and then trisecting the arc

(b) drawing an arc centered at the angle vertex, then drawing two arcs centered at the resulting points on the rays defining the angle, and finally drawing rays connecting the points at which the arcs intersect each other

(c) drawing an arc centered at the angle vertex, then drawing a line segment connecting the points at which the arc intersects the rays defining the angle, and finally trisecting the line segment

(d) none of the above means

4. Which of the following operations (a), (b), or (c) is not a “legal” thing to do when performing a construction?

(a) Drawing a circle around a specified point

(b) Drawing a circle around a randomly chosen point

(c) Drawing a straight line through two specified points

(d) All of the above operations (a), (b), and (c) are “legal”

5. Suppose you draw an arbitrary line and an arbitrary point *P* near that line. Then, using a compass, you construct a circle centered at point *P* , making the circle large enough so that it intersects the line in two points *Q* and *R* . The points *P, Q* , and *R* lie at the vertices of

(a) a right triangle

(b) an equilateral triangle

(c) an isosceles triangle

(d) none of the above

6. Suppose you want to construct a trapezoid. The exact measurement of the interior angles or side lengths is not important. The only thing that matters is that the final figure be a true trapezoid. The easiest way to start is to

(a) construct two parallel lines

(b) construct two perpendicular lines

(c) construct a circle

(d) construct two concentric circles

7. A pencil and straight edge cannot be used all by themselves to

(a) construct an arbitrary line

(b) connect two existing, specified points with a line segment

(c) copy an existing, specified line segment

(d) construct an arbitrary angle

8. In Fig. 5-15, the fact that Δ *SRP* and Δ *PQS* are inversely congruent means that they

(a) are exact mirror images of each other

(b) are the same size, and one can be laid down over the other simply by moving and rotating one of them

(c) are different sizes, but have corresponding interior angle measures that are in the same proportions

(d) are the same size, but have corresponding side lengths that might be in different proportions

9. A compass and a pencil cannot be used all by themselves to

(a) construct an arbitrary circle

(b) construct two line segments of the same length on an existing, specified line

(c) construct two concentric circles around an existing, specified point

(d) construct a straight line segment

10. Suppose you want to construct an angle whose measure is 45°. You could do this by

(a) constructing a square and then drawing its diagonal

(b) constructing a perpendicular bisector line to an existing line segment, and then bisecting one of the angles at which they intersect

(c) bisecting a 180° angle, and then bisecting one of the resulting angles

(d) any of the above methods (a), (b), or (c)

**Answers**

1. c

2. b

3. d

4. d

5. c

6. a

7. c

8. a

9. d

10. d

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