This geometry parallel lines test answer key gives the full solution and the scoring guide for each of the 9 test questions on parallel lines, transversals and proofs.
This answer key shows a complete solution and a scoring guide for each question of the parallel lines and transversals test. Award partial credit using the point breakdown listed after each solution.
Geometry Parallel Lines Test Answer Key: questions 1–5
Question 1: Name the angle pairs (2 points)
- \(\angle 4\) and \(\angle 6\) are between the lines on the same side of the transversal: same-side interior angles.
- \(\angle 1\) and \(\angle 8\) are outside the lines on opposite sides: alternate exterior angles.
Scoring: 1 point for each correct name.
Question 2: Find missing angles (2 points)
- \(m\angle 6\) = \(54^{\circ}\) (alternate interior angles are equal).
- \(m\angle 5\) = \(180-54=126\) (same-side interior angles are supplementary). \(m\angle 8\) = \(126^{\circ}\) because \(\angle 8\) and \(\angle 5\) are vertical angles. Both are \(126^{\circ}\).
Scoring: 1 point for part (a). 1 point for part (b): 0.5 for each angle.
Question 3: Corresponding angles and x (2 points)
Corresponding angles are equal: \(7x-9=4x+24\). Then \(3x=33\), so \(x=11\).
\(7(11)-9=68\) and \(4(11)+24=68\). Each angle is \(68^{\circ}\).
Scoring: 1 point for the correct equation, 1 point for \(x=11\) and both angle measures.
Question 4: Same-side interior angles and x (2 points)
Same-side interior angles are supplementary: \((3x+12)+(5x-8)=180\). Then \(8x+4=180\) and \(8x=176\), so \(x=22\).
\(3(22)+12=78\) and \(5(22)-8=102\). The angles are \(78^{\circ}\) and \(102^{\circ}\).
Scoring: 1 point for the correct equation and \(x=22\), 1 point for both angle measures.
Question 5: Decide if lines are parallel (2 points)
- Yes. The alternate interior angles are equal, so \(a \parallel b\) by the Alternate Interior Angles Converse.
- No. \(100+70=170\), which is not \(180^{\circ}\), so the same-side interior angles are not supplementary.
Scoring: 1 point per part: 0.5 for the decision and 0.5 for the reason.
Geometry Parallel Lines Test Answer Key: questions 6–9
Question 6: Proof that lines are parallel (3 points)
| Statements | Reasons |
|---|---|
| \(m\angle 2\) = \(m\angle 7\) | Given |
| \(m\angle 2\) = \(m\angle 3\) | Vertical Angles Theorem |
| \(m\angle 3\) = \(m\angle 7\) | Substitution Property of Equality |
| \(a \parallel b\) | Corresponding Angles Converse |
Scoring: 1 point for \(m\angle 2\) = \(m\angle 3\) with its reason, 1 point for \(m\angle 3\) = \(m\angle 7\), 1 point for the conclusion with the correct converse. Other valid chains also earn full credit.
Question 7: Perpendicular Bisector Theorem proof (3 points)
| Statements | Reasons |
|---|---|
| \(AM=BM\) | Definition of bisector (M is the midpoint) |
| \(m\angle PMA\) = \(m\angle PMB\) = \(90^{\circ}\) | Definition of perpendicular lines |
| \(PM=PM\) | Reflexive Property |
| \(\triangle PMA\) is congruent to \(\triangle PMB\) | SAS (two sides and the included angle) |
| \(PA=PB\) | Corresponding parts of congruent triangles are congruent |
Scoring: 1 point for the two equal sides and the equal right angles, 1 point for triangle congruence by SAS, 1 point for the conclusion with the CPCTC reason.
Question 8: Equidistant point (2 points)
\(PA=PB\), so \(4x-3=2x+13\). Then \(2x=16\), so \(x=8\).
\(PA=4(8)-3=29\) (and \(PB=2(8)+13=29\)).
Scoring: 1 point for the equation and \(x=8\), 1 point for \(PA=29\).
Question 9: Parallel avenues (2 points)
The angles are alternate exterior angles, so they are equal: \(2x+15=3x-10\). Then \(x=25\).
Each angle is \(2(25)+15=65\) degrees. The northwest angle at Cedar forms a linear pair with the northeast angle: \(180-65=115\). It measures \(115^{\circ}\).
Scoring: 1 point for \(x=25\) with the correct equation, 1 point for \(115^{\circ}\).
Scoring summary
20 points: add the points of every question of this geometry parallel lines test answer key.
How to use this geometry parallel lines test answer key
Use this geometry parallel lines test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Geometry Parallel Lines, Transversals and Proofs test answer key
Download the PDF
See every chapter on the Geometry math page.
