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

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°.

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.

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