Points Lines Planes Segments Angles Test – Geometry Math (Printable PDF)

Question 1 Reasoning with definitions (2 points)

Decide whether each statement is always, sometimes or never true, and justify briefly.

1. Two perpendicular lines form four right angles. (1 point)
2. The complement of an angle is larger than the angle. (1 point)

Question 2 Segment addition (3 points)

Point Q lies between P and R. PQ = 4x − 3, QR = 2x + 9 and PR = 48.

1. Find x. (1 point)
2. Find PQ and QR. (2 points)

Question 3 Angle addition (3 points)

Ray OB lies inside ∠AOC. m∠AOB = (5x − 4)°, m∠BOC = (3x + 12)° and m∠AOC = 128°.

1. Find x. (1 point)
2. Find m∠AOB. (1 point)
3. Find m∠BOC. (1 point)

Question 4 Complements and supplements (2 points)

Solve each problem.

1. Find the complement of a 63.5° angle. (1 point)
2. The supplement of an angle is 3 times the angle. Find the angle. (1 point)

Question 5 Vertical angles and linear pairs (3 points)

Two lines intersect at O. ∠POR = (6x − 10)° and its vertical angle ∠QOS = (4x + 20)°.

Question 6 Angle bisector (3 points)

Ray BD bisects ∠ABC. m∠ABD = (7x − 9)° and m∠DBC = (4x + 12)°.

1. Find x. (1 point)
2. Find m∠DBC. (1 point)
3. Find m∠ABC. (1 point)

Question 7 Midpoint coordinate (2 points)

On a number line, P is at −8.5 and Q is at 5.5. Find the coordinate of the midpoint of PQ and the length PQ.

Question 8 Water station on a trail (2 points)

A straight trail runs from trailhead T to summit S, and TS = 7.8 miles. A water station W is at the midpoint of TS. A bench B is 1.15 miles from T on the trail. Find TW and BW.