Geometry Basic Rules Practice Test

Before taking this quiz, review basic geometry rules about:

• Points and Line Help
• Angles and Distances Help
• More About Lines and Angles Help 

Geometry Basic Rules Practice Test

1. An angle measures 30°. How many radians is this, approximately? You can use a calculator if you need it.

(a) 0.3333 rad

(b) 0.5000 rad

(c) 0.5236 rad

(d) 0.7854 rad

2. Consider a half-open line segment PQ , which includes the end point P but not the end point Q. Let line L ₁ be the perpendicular bisector of PQ , and suppose that L ₁ intersects the line segment PQ at point Q ₁ . Now imagine the half-open line segment PQ ₁ , which includes point P but not point Q ₁ . Let line L ₂ be the perpendicular bisector of PQ ₁ , and suppose that L ₂ intersects the line segment PQ ₁ at point Q ₂ . Imagine this process being repeated, forming perpendicular bisectors L ₃ , L ₄ , L ₅ , . . ., crossing line segment PQ at points Q ₃ , Q ₄ , Q ₅ , . . ., which keep getting closer and closer to P . After how many repetitions of this process will the perpendicular bisector pass through point P ? Draw a picture of this situation if you cannot envision it from this wording.

(a) The perpendicular bisector will never pass through P , no matter how many times the process is repeated

(b) The question cannot be answered without more information

(c) This question is meaningless, because a half-open line segment cannot have a perpendicular bisector

(d) This question is meaningless, because a half-open line segment has infinitely many perpendicular bisectors

3. Suppose that a straight section of railroad crosses a straight stretch of highway. The acute angle between the tracks and the highway center line measures exactly 1 rad. What is the measure of the obtuse angle between the tracks and the highway center line?

(a) This question cannot be answered without more information

(b) 1 rad

(c) π/2 rad

(d) π − 1 rad

4. An open line segment

(a) contains neither of its end points

(b) contains one of its end points

(c) contains two of its end points

(d) contains three of its end points

5. Two different, straight lines in a Euclidean plane are parallel if and only if

(a) they intersect at an angle of π rad

(b) they intersect at an angle of 2π rad

(c) they intersect at one and only one point

(d) they do not intersect at any point

6. Suppose you choose two points at random in a plane. How many Euclidean line segments exist that connect these two points?

(a) None

(b) One

(c) More than one

(d) Infinitely many

7. The measures of vertical angles between intersecting lines

(a) always add up to 90°

(b) always add up to 180°

(c) always add up to 360°

(d) depend on the angle at which the lines intersect

8. Two lines are orthogonal. The measure of the angle between them is therefore

(a) 0°

(b) π rad

(c) 2π rad

(d) π/2 rad

9. When an angle is bisected, two smaller angles are formed. These smaller angles

(a) are obtuse

(b) measure 90°

(c) have equal measure

(d) have measures that add up to 180°

10. Suppose two straight lines cross at a point P , and the lines are not perpendicular. Call the measures of the obtuse vertical angles x ₁ and x ₂ . Which of the following equations is true?

(a) x ₁ < x ₂ (that is, x ₁ is smaller than x ₂ )

(b) x ₁ > x ₂ (that is, x ₁ is greater than x ₂ )

(c) x ₁ = x ₂

(d) x ₁ + x ₂ = 180°

Answers

1. c

2. a

3. d

4. a

5. d

6. b

7. d

8. d

9. c

10. c