Geometry Practice Test: Parallel Lines and Transversals
- Parallel Lines and Transversals
- 10 questions
- 13 minutes
These questions cover the angle pairs formed when a transversal crosses two lines, both when the lines are parallel and when you must decide whether they are. Tip: first name the angle pair, then decide whether it is congruent or supplementary.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
Two parallel lines are cut by a transversal. A pair of alternate interior angles measure (7x − 18)° and (4x + 30)°.
What is the measure of each of these angles?
Correct answer: C
Alternate interior angles are congruent: 7x − 18 = 4x + 30, so x = 16 and each angle is 7(16) − 18 = 94°. The choice 16° is only the value of x, and 86° is the supplement of 94°.
-
Question 2
Two parallel lines are cut by a transversal. Two same-side exterior angles measure (5x + 8)° and (3x + 12)°.
What is the value of x?
Correct answer: C
Same-side exterior angles are supplementary: 8x + 20 = 180, so x = 20. Setting the angles equal gives x = 2, but these angles are not congruent.
-
Question 3
Two parallel lines are cut by a transversal that is not perpendicular to them. Which pair of angles must be supplementary?
Correct answer: B
Same-side (consecutive) interior angles add up to 180°. The other three pairs are congruent, and congruent angles are supplementary only when both are 90°.
-
Question 4
Lines a and b are cut by transversal t. Two same-side interior angles measure 72° and 108°.
Which conclusion is justified?
Correct answer: D
The angles add up to 72° + 108° = 180°, and by the converse of the Same-Side Interior Angles Theorem the lines are parallel. Nothing in the data says any angle is 90°, so perpendicularity does not follow.
-
Question 5
In a plane, lines p and q are cut by a transversal. A pair of alternate interior angles measure 63° and 65°.
Which statement is true?
Correct answer: A
If the lines were parallel, the alternate interior angles would be congruent. Since 63° ≠ 65°, the lines are not parallel, and two non-parallel lines in a plane intersect. Their angle of intersection is only 2°, so they are not perpendicular.
-
Question 6
Two parallel lines are cut by a transversal. One same-side interior angle is 4 times as large as the other.
What is the measure of the smaller angle?
Correct answer: B
The angles are supplementary: x + 4x = 180, so x = 36° and the larger angle is 144°. Choosing 144° gives the larger angle instead of the smaller one.
-
Question 7
In a plane, line a is parallel to line b, and line t is perpendicular to line a.
What is the measure of the angle between line t and line b?
Correct answer: A
A transversal that is perpendicular to one of two parallel lines is perpendicular to the other one too, because corresponding angles are congruent: both are 90°.
-
Question 8
In a plane, lines a and b are both perpendicular to line t. What is the relationship between a and b?
Correct answer: D
Line t forms 90° corresponding angles with a and with b, so by the converse of the Corresponding Angles Postulate the lines are parallel. Skew lines cannot exist inside a single plane.
-
Question 9
Two parallel lines are cut by a transversal. A pair of alternate exterior angles measure (9x − 21)° and (6x + 18)°.
What is the measure of each acute angle formed by the transversal and either parallel line?
Correct answer: C
Alternate exterior angles are congruent: 9x − 21 = 6x + 18 gives x = 13, so these angles measure 96°. They are obtuse, so the acute angles are 180° − 96° = 84°. The trap 96° answers a different question.
-
Question 10
The Corresponding Angles Postulate says: "If two parallel lines are cut by a transversal, then corresponding angles are congruent."
Which statement is the converse of this postulate?
Correct answer: B
A converse swaps the hypothesis and the conclusion: congruent corresponding angles now lead to parallel lines. The first option is the contrapositive and the last one is the inverse.
Questions you leave blank are not counted as wrong.
More Math tests
MathGeometry Practice Test: Triangle Congruence (SSS, SAS, ASA, AAS, HL)Triangle Congruence10 questions13 min MathGeometry Practice Test: Angles, Parallel Lines and Proof ReasoningAngles, Parallel Lines and Proof15 questions18 minMathGeometry Practice Test: Triangle Congruence and SimilarityTriangle Congruence and Similarity15 questions18 minMathGeometry Practice Test: Right Triangles and TrigonometryRight Triangles and Trigonometry15 questions20 minMathGeometry Practice Test: Circle Arcs, Angles and ChordsCircles: Arcs, Angles and Chords15 questions18 minMathGeometry Practice Test: Area, Volume and Coordinate GeometryArea, Volume and Coordinate Geometry15 questions20 minMathGeometry Practice Test: Similar TrianglesSimilar Triangles10 questions14 min