Points, Lines, Planes, Segments and Angles: Geometry Math Test Answer Key – PDF Download

Geometry Foundations Test Answer Key: questions 1–5

Question 1: Undefined terms and definitions (2 points)

1. Point, line and plane.
2. A ray is a part of a line that consists of one endpoint and all the points of the line extending in one direction from it.

Scoring: 1 point for all three terms; 1 point for a definition that includes one endpoint and extension in one direction only.

Question 2: Naming rays and points (2 points)

1. Ray BC (endpoint first).
2. Ray BA and ray BC share endpoint B and form line AC: ray BA and ray BC.

Scoring: 1 point for each part. Award the first point only if the endpoint is named first.

Question 3: Segment addition (3 points)

1. \((2x+3)+(3x-1)=37\), so \(5x+2=37\) and \(5x=35\). x = 7.
2. \(KL=3(7)-1=20\). KL = 20.

Scoring: 1 point for the correct equation, 1 point for x = 7, 1 point for KL = 20.

Question 4: Midpoint (2 points)

1. \(5x-4=3x+8\), so \(2x=12\) and x = 6.
2. \(RN=5(6)-4=26\) and \(NS=3(6)+8=26\), so \(RS=26+26=52\). RS = 52.

Scoring: 1 point for each part.

Question 5: Angle addition (3 points)

1. \((3x+7)+(5x-1)=118\), so \(8x+6=118\) and \(8x=112\). x = 14.
2. \(m\angle BOC\)\(=5(14)-1=69^{\circ}\). 69°.

Scoring: 1 point for applying the Angle Addition Postulate, 1 point for x = 14, 1 point for 69°.

Geometry Foundations Test Answer Key: questions 6–8

Question 6: Complement problem (2 points)

Let the complement be \(y^{\circ}\). The angle is \(4y^{\circ}\) and they add to \(90^{\circ}\): \(y+4y=90\), so \(5y=90\) and \(y=18\).

Complement 18°; angle 72°. Check: \(4\times 18=72\) and \(72+18=90\).

Scoring: 1 point for a correct equation, 1 point for both measures.

Question 7: Vertical angles and linear pairs (3 points)

1. Vertical angles are congruent: \(6x-8=4x+14\), so \(2x=22\) and x = 11.
2. \(m\angle 1\)\(=6(11)-8=58^{\circ}\). 58°.
3. Angles 1 and 2 are a linear pair, so they are supplementary: \(m\angle 2\)\(=180-58=122^{\circ}\). 122°.

Scoring: 1 point for each part; part (c) needs the measure and the linear pair reason.

Question 8: Angle bisector (3 points)

1. A bisector makes equal angles: \(4x-6=2x+14\), so \(2x=20\) and x = 10.
2. Each part is \(4(10)-6=34^{\circ}\), so \(m\angle ABC\)\(=34+34=68^{\circ}\). 68°.
3. \(68^{\circ}< 90^{\circ}\) (less than a right angle), so the angle is acute.

Scoring: 1 point for each part.

Scoring summary

How to use this geometry foundations test answer key

Use this geometry foundations test answer key to score the test fairly and to see which skills need more practice.

Printable PDF · Test Answer Key

Geometry Points, Lines, Planes, Segments and Angles test answer key

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