Geometry Points, Lines, Segments and Angles Test Solutions and Scoring (PDF)

Geometry math test solutions: Points, Lines, Segments and Angles – Maths PDF

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This basics test answers for Geometry covers points, lines, segments and angles (Common Core G-CO.A.1), with a free PDF to print.

Use this answer key and scoring guide for the segments and angles test. Each solution shows the full work, and the scoring note tells how the points are split between method and final answer. Partial credit is listed so that grading stays consistent from one paper to the next.

Geometry · Common Core State Standards: G-CO.A.1

Basics test answers: worked solutions

Question 1 – Segment addition [2 pts]

PQ = 15 and QR = 18.

\((3x – 3) + (2x + 6) = 33\)

\(5x + 3 = 33\)

\(x = 6\)

\(PQ = 3(6) – 3 = 15\)

x = 6, PQ = 15

Scoring: 1 point for the equation, 1 point for correct x and PQ.

Question 2 – Midpoint and length [3 pts]

Midpoint M(1, 1).

\(\left( \frac{-4 + 6}{2}, \frac{3 + (-1)}{2} \right) = (1, 1)\)
\(EF = \sqrt{(6 – (-4))^{2} + (-1 – 3)^{2}} = \sqrt{100 + 16} = \sqrt{116} = 2\sqrt{29}\)

(a) (1, 1); (b) \(2\sqrt{29}\) units

Scoring: (a) 1 point. (b) 1 point for the distance setup, 1 point for the simplified radical.

Question 3 – Angle bisector [2 pts]

\(2x + 7 = 5x – 20\)

\(27 = 3x\)

\(x = 9\)

\(2(9) + 7 = 25\), so \(m\angle ABC = 50^{\circ}\)

x = 9, m∠ABC = 50°

Scoring: 1 point for equating the halves, 1 point for x and the angle measure.

Question 4 – Complement and linear pair [2 pts]

\(x + 12 + 2x – 6 = 90\), \(3x = 84\), \(x = 28\)
\(a + 4a = 180\), \(a = 36\), so the angles are \(36^{\circ}\) and \(144^{\circ}\)

(a) x = 28; (b) 36° and 144°

Scoring: 1 point each part for a correct equation and answer.

Question 5 – Definitions [3 pts]

A circle is the set of all points in a plane at a given distance from a fixed point (the center).
Perpendicular lines are two lines that intersect to form right (\(90^{\circ}\)) angles.
A segment has two endpoints and a finite length; a ray has one endpoint and extends forever in one direction.

Scoring: 1 point per definition. Accept equivalent wording, but the circle definition must mention a fixed center and a constant distance.

Question 6 – Find an endpoint [2 pts]

\(\frac{13 + x}{2} = 7\) gives \(x = 1\).

\(\frac{4 + y}{2} = -2\) gives \(y = -8\).

B(1, -8)

Scoring: 1 point for each coordinate.

Question 7 – Clock angle [2 pts]

At 5:00 the hands are 5 hours apart: \(5 \cdot 30^{\circ} = 150^{\circ}\).

At 10:30 the minute hand is at \(180^{\circ}\) and the hour hand is at \(10.5 \cdot 30^{\circ} = 315^{\circ}\), a difference of \(135^{\circ}\).

150° and 135°

Scoring: 1 point for each time.

Question 8 – Equal distances [2 pts]

Distance from the center: \(\sqrt{(5 – 2)^{2} + (3 + 1)^{2}} = \sqrt{9 + 16} = 5\).

The distance equals the radius, so the point is on the circle.

Scoring: 1 point for the distance, 1 point for the conclusion.

Question 9 – Pipeline markers [2 pts]

\(\frac{4.5 + 29.5}{2} = 17\).

\(29.5 – 4.5 = 25\), so each distance is \(12.5\) miles.

Mile 17, 12.5 miles from each marker

Scoring: 1 point for the midpoint, 1 point for the distance.

Total score

Total

20 points

Key facts behind this basics test answers

Key facts

Point, line and plane are undefined terms; segments, rays and angles are defined from them.
Segment addition: if B is between A and C, then AB + BC = AC.
A midpoint at coordinate (a + b)/2 splits a segment into two congruent segments.
Angle addition: m∠ABD + m∠DBC = m∠ABC when ray BD is inside the angle.
A circle is all points in a plane at one fixed distance (the radius) from the center.

How to use this basics test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

Download the basics test answers as a PDF with the button below and keep it with your notes.

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