Points, Lines, Planes, and Angle Relationships: math test, Grade 10 – download the PDF

1 Vocabulary / 3 pts

(a) How many points are needed to determine one line? (b) How many non-collinear points are needed to determine one plane? (c) What is the difference between segment \(\overline{AB}\) and ray \(\overrightarrow{AB}\)?

2 Segment addition / 3 pts

Point \(S\) is between \(R\) and \(T\). \(RS = (4x - 3)\) cm, \(ST = (2x + 9)\) cm and \(RT = 48\) cm. Find \(x\), \(RS\), and \(ST\).

3 Coordinates / 4 pts

Let \(P(-2, -1)\) and \(Q(10, 8)\). (a) Find the midpoint of \(\overline{PQ}\). (b) Find \(PQ\).

4 Adding angles / 4 pts

Rays \(OB\) and \(OC\) lie inside \(\angle AOD\) with \(m\angle AOD = 132^\circ\), \(m\angle AOB = (2x + 4)^\circ\), \(m\angle BOC = (3x - 6)^\circ\) and \(m\angle COD = (x + 14)^\circ\).

(a) Find \(x\). (b) Find the three angle measures. (c) Does \(OB\) or \(OC\) bisect \(\angle AOD\)?

5 Vertical angles / 3 pts

Two lines intersect as shown. \(m\angle 1 = (7x - 4)^\circ\) and \(m\angle 3 = (4x + 23)^\circ\).

Find \(x\), \(m\angle 1\), and \(m\angle 2\).

6 Construction / 3 pts

Explain how to construct the perpendicular bisector of a segment \(\overline{AB}\) with a compass and straightedge, and say what is true of the point where it meets \(\overline{AB}\).