Parallel Lines, Transversals and Proofs: Geometry Math Test – PDF Download

Question 1: Name the angle pairs (2 points)

Lines \(a\) and \(b\) are cut by transversal \(t\). Name each pair of angles.

1. \(\angle 4\) and \(\angle 6\) (1 point)
2. \(\angle 1\) and \(\angle 8\) (1 point)

Question 2: Find missing angles (2 points)

Lines \(a\) and \(b\) are parallel and \(m\angle 3\) = \(54^{\circ}\).

1. Find \(m\angle 6\). (1 point)
2. Find \(m\angle 5\) and \(m\angle 8\). (1 point)

Question 3: Corresponding angles and x (2 points)

Lines \(a\) and \(b\) are parallel. Find \(x\) and the measure of each marked angle.

Question 4: Same-side interior angles and x (2 points)

Lines \(a\) and \(b\) are parallel. Two same-side interior angles measure \((3x+12)^{\circ}\) and \((5x-8)^{\circ}\). Find \(x\) and the measure of each angle.

Question 5: Decide if lines are parallel (2 points)

For each case, decide whether \(a\) and \(b\) must be parallel. Give a reason.

1. Alternate interior angles \(\angle 3\) and \(\angle 6\) each measure \(83^{\circ}\). (1 point)
2. Same-side interior angles measure \(100^{\circ}\) and \(70^{\circ}\). (1 point)

Question 6: Proof that lines are parallel (3 points)

Given \(m\angle 2\) = \(m\angle 7\), prove \(a \parallel b\). Write a two-column proof.

Question 7: Perpendicular Bisector Theorem proof (3 points)

Given: line \(\ell\) is the perpendicular bisector of \(\overline{AB}\) at \(M\), and \(P\) is on \(\ell\). Prove \(PA=PB\).

Question 8: Equidistant point (2 points)

Point \(P\) is on the perpendicular bisector of \(\overline{AB}\). \(PA=4x-3\) and \(PB=2x+13\). Find \(x\) and \(PA\).

Question 9: Parallel avenues (2 points)

Elm Avenue and Cedar Avenue are parallel. Main Street crosses both. The northeast angle at Elm measures \((2x+15)^{\circ}\) and the southwest angle at Cedar measures \((3x-10)^{\circ}\). Find \(x\) and the northwest angle at Cedar.

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