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Review of Geometry I
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Review of Geometry I
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Full Book Quiz
1. What is the sum of four angles if two are complementary and two are supplementary?
180 degrees
360 degrees
270 degrees
90 degrees
2. How many noncolinear points are required to determine a plane?
Two
An infinite number
Four
Three
3. How many dimensions are spanned by intersecting lines?
Two
Three
One
More information is needeed
4. How many times can two lines intersect?
Zero
One
Two
Zero or One
5. When is a line
l
perpendicular to a plane?
When
l
and the plane intersect at one point
When
l
and the plane don't intersect
When every line in the plane that contains the intersection point of the
l
and the plane is perpendicular to
l
When
l
intersects evey line in the plane at a 90 degree angle
6. Which of the following figures is two-dimensional?
A ray
A polygon
A point
A sphere united with its interior points
7. Which of the following angles must be an exterior angle?
A 120 degree angle
An angle whose complement is 75 degrees
A right angle
A 230 degree angle
8. Adjacent angles can be all but which of the following?
Complementary
Vertical
Acute
Supplementary
9. When two lines intersect, they form two pairs of what?
Vertical angles
Adjacent angles
Supplementary angles
Right Angles
10. Angles ABC and DBE are which of the following?
Figure 1
Vertical
Complementary
Supplementary
Vertical and supplementary
11. There exists a line
l
and two distinct points not on
l.
How many lines parallel to
l
can be drawn containing those two points?
One
Two
Zero
Either zero or one; it depends on the locations of the points.
12. Given that lines
l
and
m
are parallel, what is the measure of angle 1?
Figure 2
30 degrees
60 degrees
120 degrees
Impossible to Calculate
13. When a transversal cuts three parallel lines, how many pairs of supplementary angles are formed?
12
18
24
36
14. If line
l
bisects angle ABC, what is the measure of angle 1?
Figure 3
110 degrees
70 degrees
55 degrees
35 degrees
15. The distance from a point to a line is what?
The length of any segment drawn between the point and the line
The length of another line perpendicular to the first line, containing the point
The length of the segment perpendicular to the line with one endpoint at the point and one endpoint on the line
Any of the above -- they're all the same
16. How many lines can be drawn that are oblique to a given line?
An infinite number
One
Zero
Not enough information to tell
17. What can you conclude about two lines if the pairs of vertical angles created at their intersection are supplementary?
The lines are parallel
The lines are perpendicular
The lines are oblique
Nothing
18. How many midpoints does a segment have?
Zero
One
An infinite number
Not enough information to tell
19. When a straight angle is bisected, two angles are formed. What can be said about these angles?
They are supplementary
They are adjacent
They are right
All of the above
20. If a right angle is bisected, and one of the new angles formed by the bisector is trisected, what is the measure of one of the three newest angles?
30 degrees
22.5 degrees
15 degrees
10 degrees
21. If the starting point of a curve is the same as its ending point, what is the curve called?
A simple closed curve
A polygon
A surface
A closed curve
22. The following figure is which of the following?
Figure 4
A closed curve
A simple closed curve
A polygon
Either a closed curve or a simple closed curve
23. What is the greatest number of interior diagonals a concave pentagon can have?
Three
Four
Five
Zero
24. If a quadrilateral and a traingle share one side, what is the name of the polygon created by their union?
Hexagon
Heptagon
Quadrilateral
Their union doesn't necessarily result in a polygon
25. If the sum of the exterior angles of a polygon equals 360 degrees, how many sides does the polygon have?
Four
Three
More than six
Not enough information to tell
26. Which of the following polygons is always convex?
A triangle
A quadrilateral
A pentagon
A dodecagon
27. How many triangles must be combined to assemble a heptagon?
Two
Three
Five
Triangles cannot be combined to form a heptagon
28. If the interior angles of a polygon sum to 720 degrees, how many vertices does that polygon have?
Four
Five
Six
The sum of the interior angles of a polygon never equals 720 degrees
29. A rectangle is an example of what?
An equilateral polygon
A parallelogram
A closed curve
Answers (b) and (c)
30. Given that the quadrilateral pictured is a parallelogram, what is the measure of angle 1?
Figure 5
30 degrees
60 degrees
150 degrees
Not enough information to tell
31. Given that the quadrilateral pictured is a parallelogram, what is the measure of angle 2?
Figure 6
40 degrees
80 degrees
100 degrees
Not enough information to tell
32. What polygon has 540 degrees of interior angles and 14 diagonals?
A pentagon
A heptagon
Any polygon
There is no polygon with such characteristics
33. If the sum of the lengths of the bases of a trapezoid is 12, what is the length of its median?
12
6
4
8
34. If a central angle is 35 degrees, what is the measure of the major arc whose endpoints are the intersection points of the central angle and the circle?
35 degrees
145 degrees
325 degrees
395 degrees
35. The radius of a circle is 14. How long is the chord whose endpoints are the same as the endpoints of a 180 degree arc?
7
14
28
Not enough information
36. If a sector is partially bound by the diameter of a circle, what is the measure of the arc that completes the boundary of the sector?
360 degrees
180 degrees
90 degrees
270 degrees
37. Which of the following sets of figures do
not
determine a circle?
A center and a diameter
A center and a secant line
A diameter and a tangent line
A center and a chord
38. If a secant line contains the center of a circle as well as the midpoint of a chord of the circle, and these two points are different, what is the relationship between the secant line and the chord?
The secant line and the line that contains the chord are parallel.
The secant line contains the chord.
The secant line is the perpendicular bisector of the chord.
There is no special relationship between the secant line and the chord.
39. The angle created by a tangent line and the radius of a circle whose endpoint is the point of tangency is bisected. What is the measure of the two new angles created?
90 degrees
180 degrees
45 degrees
30 degrees
40. A hexagon is circumscribed about a circle. How many radii can be drawn that are perpendicular to a side of the hexagon?
Zero
Five
Six
12
41. How many curves exist in a surface?
Zero
One
However many dimensions the surface has
An infinite number
42. The bases of a prism are octagons. How many lateral edges are there in the prism?
Four
Eight
Twelve
Sixteen
43. The lateral faces of a prism could be which of the following?
Parallelograms
Squares
Rhombuses
Any of the above
44. If planes are oblique, what is their intersection?
A point
A line
A plane
A segment
45. Which of the following is not necessarily a convex simple closed surface?
A cone
A polyhedron
A pyramid
A right prism
46. At how many points can a line and a surface intersect?
Zero
One
Three
They can intersect at an infinite number of points.
47. What is the least number of polygons needed to form the surface of a polyhedron?
One
Two
Three
Four
48. When does the altitude of a pyramid lie within one of the faces of the pyramid?
When the pyramid is a regular pyramid
Only when the altitude is one of the lateral edges of the pyramid
When a line can be drawn that is perpendicular to the plane of the base and contains the vertex as well as a point on the polygon that bounds the base
Only when the base of the pyramid is a triangle
49. When are two planes perpendicular?
When one plane contains a line which is perpendicular to the other plane
When their intersection is a line
When every line in one plane is perpendicular to every line in the other plane
When any given third plane either intersects both planes or neither
50. When spheres intersect one another, their intersection could be
A point
A circle
A plane
A point or a circle
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