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GEOMETRY CLASSWORK ON LESSON 1-2:
POINTS, LINES, AND PLANES
Student name : __________________
Period:______
EXERCISE I:
Refer to the diagram below
1)
a) Name line AB in another way
b) Give two other names for plane Q
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c) Why is EBD not an acceptable name for plane Q?
2) Are the following sets of points collinear ?
a) E, B, and F
b) Line DB and line FC
c) Line AC and line ED
d) Line AE and line DC
e) F,
A,
B,
and C
f) F,A,B,and D
g) Plane Q and line EC
h) Line FB and line BD
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EXERCISE II:
Find the intersection of the following lines and planes in the figure above
a) Line GK and line LG
b) Planes GLM and LPN
d) Planes GHPN and KJP
e) Planes HJN and GKL
f) Line KP and plane KJN
g) Line KM and plane GHL
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EXERCISE III:
Refer to the diagram above
a) Name plane P in another way
b) Name plane Q in another way
c) What is the intersection of planes P and Q?
d) Are A , B and C collinear?
e) Are D,A,B, and C coplanar?
f) Are D ,B and C collinear?
g) What is the intersection of line AB and line DC
h) Are planes P and Q coplanar
i) Are line AB and plane Q coplanar?
j) Are B and C collinear?
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EXERCICE IV: Points, Lines, and Planes
Use the figure below to answer questions 1- 6.
1)Name the plane with 3 letters: ______ (2) Line AC intersects the plane at what point? _____
3) Line HG and line GE intersect at what point? ____ (4) Name 3 collinear points: ______
5) Name a point NOT on the plane: _____ (6) Are points F, D, E and B coplanar? _____
EXERCISE V:
Use the figure above to answer questions 1-7.
1) How many planes are there in the figure? _____
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2) How many planes contain H? ______
3) Name three collinear points: ______
4) Name two points not on the Plane XBN: _____
5) Name four points that are coplanar: _______
6) Name a line that does NOT contain J: ______
7) Name three non-collinear points: ______
EXERCISE VI:
Draw 
AB
EXERCISE VII: Draw 
, 
, and AC .Use a straightedge.
CD
AB
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EXERCISE VIII:
Name a point that is collinear with the given points
_ B and E:
_ C and H:
_ D and G:
_ A and C:
_ H and E:
_ G and B:
EXERCISE IX:
Name a point that is coplanar with the given points
_ M, N, R:
_ M, N, O:
_ M, T, Q:
_ Q, T, R:
_ T, R, S:
_ Q, S, O:
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EXERCISE X: Determine if the pairs of lines appear to be parallel, perpendicular, or skew. It’s OK to write
symbols for parallel and perpendicular.
a)Line BF and line AE are ________________ b)Line CG and line HG are ______________
c)Line AD and line AE are _______________
d) Line FG and line EH are ____________
e)Line AD and line HG are _______________ f) line HG and line BF are _______________
EXERCISE XI: Use the diagram below.
a. Name the intersection of line BE and line CD .
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b. Name the intersection of line BE and plane A.
c. Name the intersection of line DB and plane F.
d. Name the intersection of plane A and F.
EXERCISE XII: Use the diagram below. Be sure to use correct notation.
a.
Name any four points.
b. Name any two lines.
c. Name all the points on plane P.
d. Name three collinear points
e. Name the plane that contains point A
f.. Decide whether the following statement is true or false.
“Points F, D, and B are coplanar.”
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EXERCISE XIII: Use the figures to name the following.
1. Three collinear points ____________
2. Four coplanar points ____________
3. A plane containing E ____________
4. Two points and a line that lie in plane T ____________
5. Two planes that contain l ____________
6. The intersection of line TV and line US ____________
7. The intersection of
and plane
8. The intersection of TU and UV ____________
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EXERCISE XIV: Refer to the diagram:
a) Name 2 planes that intersect in line HG . ____________
b) Are the points A, B, C and D collinear? ____________
c) Are the points A, B, C and D coplanar? ____________
d) Name 2 planes that do not intersect. ___________
e) Name 3 lines that intersect at C. ____________
EXERCISE XV: Complete with always, sometimes, or never.
1) Three points ______________ determine a plane.
2) Two points ______________ lie in exactly one line.
3) Three points ______________ lie in exactly one line.
4) Three collinear points ______________ lie in exactly one plane.
5) Two planes ______________ intersect.
6) Two intersecting planes ______________ intersect in exactly one point.
7) Two intersecting lines ______________ intersect in exactly one point.
8) Two lines ______________ intersect in exactly one point.
9) Two intersecting lines ______________ lie in exactly one plane.
10) A line and a point not on that line ______________ lie in more than one plane.
11) A line ______________ contains exactly one point.
12) When A and B are in a plane, 
is ______________ in that plane.
AB
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SELECTIVE RESPONSE
1. Identify an example of an undefined term:
A. a point
B. collinear points
C. non-collinear points D. coplanar points
E. non-coplanar points
2. All of the following are correct names for the line except:
3. The ceiling of our classroom is an example of a:
A. point
B. line
C. plane
D. defined term
E. none of the
above
4. The meeting place of two geometric objects is called:
A. a point
B. a line
C. a plane
D. collinear
E. an intersection
5. How many non-coplanar points define space?
6. How many non-coplanar points define space?
A. 1
B. 2
C. 3
D. 4
E. 5
7. How many points define a line?
A. 1
B. 2
C. 3
D. 4
E. 5
8. How many non-collinear points define a plane?
A. 1
B. 2
C. 3
D. 4
E. 5
9. The intersection of two planes is a:
A. point
B. segment
C. line
D. ray
E. plane
10. The intersection of a line and a plane is a:
A. point
B. segment
C. line
D. ray
E. plane
11. All of the following statements are true except
A. Two intersecting lines meet at a point.
B. Opposite rays share an endpoint.
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C. Adjacent angles share a side and a vertex.
D. Co-planar points are points on the
same plane.
E. Obtuse angles measure less than 90 degrees.
12)All of the following statements are true except:
A. Opposite rays share an endpoint.
B. The intersection of two planes is a point.
C. Four non-coplanar points determine space.
D. Obtuse angles measure more than 90
degrees.
E. Congruent segments have the same length.
13) Which of the following best describes a counterexample to the assertion below:
Two lines in a plane always intersect in exactly one point.
A. coplanar lines
B. parallel lines C. perpendicular lines D. intersecting lines E. none of the
above
14) Which of the following is an example of an undefined term?
A. a ray
B. an angle bisector
C. a midpoint of a segment D. a line
E. vertical angles
15)All of the following statements are true except:
A. Two intersecting lines meet at a point.
B. Opposite rays share an
endpoint.
C. Adjacent angles share a side and a vertex.
D. Co-planar points are points on the same plane. E. Obtuse angles measure less than 90
degrees.
16: In general, a plane is represented by a ______.
A) rectangle or parallelogram
B) lines
C) points
D) sphere
17: The line drawn through two different points in a plane _______ lies in the plane containing the
two points. A) sometimes completely, sometimes partially
B) always partially
C) always
completely
18: The relationships between points and lines in a plane are called _____.
A) linear properties
B) planar properties
C) surface properties
D) incidence
properties
19: The number of surfaces that a cylinder contains is _____.
A) three
B) two
C) one
20: The symbol '||' represents
A) perpendicular lines
B) intersecting lines
C) parallel lines
D) finite
lines
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21: Two intersecting lines in a plane have ________ common point(s). A) only three B) only one
C) only two C) many
22: _____ line (or lines) can be drawn through two different points in a plane.
A) Many
B) Only one
C) Two
D) Only three
23: Two different lines in a plane having a common point are called _____.
A) intersecting lines
B) common lines
C) parallel lines
D) point lines
24) Which of the following are skew lines?
a) RY and YR
b) PS and PQ
c) QR and RY
d) RY and PS
25) Points A and B are collinear. This means that points A and B...
 a) Lie in one plane b) Lie in one triangle c) Lie on one line d) Lie in any quadrilateral
26) Points C and D are coplanar. This means that points C and D...
a) Lie in one plane b) Lie in one triangle c) Lie on one line d) Lie in any
quadrilateral
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EXERCISE:
True/False, Always/Sometimes/Never
Classify each statement as TRUE or FALSE.
1. Three given points are always coplanar.
2. A line that intersects a segment at its midpoint is the perpendicular bisector.
3. The contrapositive of a true conditional is sometimes false.
4. An acute angle inscribed in a circle must intercept a minor arc.
5. In a plane the locus of points equidistant from M and N is the midpoint of MN .
6. Through a point not on a line there are two lines parallel to the given line.
7. A triangle with vertices (a, 0), (-a, 0), and (0, a) is equilateral.
8. Point, line, and plane are defined terms in Euclidean geometry.
9. A point lies on the bisector of  ABC if and only if it is equidistant from A and C.
10. A triangle with sides of length 2x, 3x, and 4x must be obtuse.
11. Collinear points are also coplanar.
12. If two rays have the same endpoint then they are opposite rays.
13. It is possible for two angles to be adjacent, congruent, and complementary.
14. If a = b and b = c, then a = c.
15. The intersection of two planes can be a single point.
16. If AB = BC, then B is the midpoint of AC
.
17. Two lines that have no points in common must be parallel.
18. A triangle is isosceles if it is equilateral.
19. If a  c and b  c , then a and b are always parallel.
20. The diagonals of a rhombus bisect each other.
21. Through any two points there is exactly one line.
22. If two planes intersect, then thier intersection can be a point.
23. If two angles of one triangle are congruent to two angles of another triangle, then the triangles
are similar.
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24. Semicircles can be adjacent arcs.
25. The maesure of the arc formed by two adjacent arcs is the sum of the measures of the arcs.
26. If the exterior sides of two adjacent angles lie on a line then the sum of their measures is
90.
27. Two points determine a plane.
28. Space contains at least four points.
29. Two lines can intersect in more than one point.
1stSemesterReviewTrueFalse.nb 1
30. If an angle and two sides of one triangle are congruent to an angle and two sides of
another triangle, then the triangles are congruent.
31. Two angles complementary to the same angle are congruent to each other.
32. Vertical angles may be adjacent angles.
33. If two angles are compmentary and congruent, then each has a measure of 45.
34. Two vertical angles may be supplementary.
35. If the sum of the measures of three angles is 90, then the angles are complementary.
36. If the exterior sides of two adjacent angles are perpendicular, then the angles are
complementary.
37. Skew lines are noncoplanar lines.
38. It is possible for two planes to be skew.
39. If two lines are cut by a transversal, then corresponding angles are congruent.
40. Two lines perpendicular to the same line are parallel to each other.
41. Two lines parallel to the same line are parallel to each other.
42. Another name for an if-then statement is a conditional.
43. The converse of a conditional is formed by negating the hypothesis ad the conclusion.
44. The converse and the inverse of a conditional are logically equivalent.
45. "If  A  B , then  B  A is an example of the Transitive Property.
46. A conjecture is a conclusion based on observation.
47. Vertical an—gles are congruent.
48. A scalene triangle may be obtuse.
49. An equilateral triangle is also isosceles.
50. An isoscles right triangle is a 45-45-90 triangle.
51. The measure of an exterior angle of a triangle is equal to the sum of the measures of the
two remote interior angles.
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52. Corresponding parts of congruent triangles are congruent.
53. If two angles of one triangle are congruent to two angles of another triangle, then the third
angles are complementary.
54. In a triangle, the longest side is opposite the smallest angle.
55. In an isoscles triangle, the median from any angle is also the perpendicular bisector of the
opposite side.
56. Concurrect lines are two or more lines that intersect in one point.
57. The medians of a triangle are concurrent at a point called the centroid.
58. The lines that contain the altitudes are concurrent at a point called the orthocenter.
59. The orhtocenter is always located in the interior of a triangle.
60. The perpendicular bisectors of the side are concurrent at a point called the circumcenter.
61. The centroid, othocenter, and circumcenter all lie on Euler's line.
62. A proportion is an equation stating that two ratios are equal.
1stSemesterReviewTrueFalse.nb 2
63. A Golden Rectangle is a rectangle that can be divided into two equal squares.
64. The geometric mean of two numbers can be negative.
65. The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that
are similar to each other.
66. The numbers 6, 8, and 10 are primitive Pythagorean triples.
67. If the square of the longest side of a triangle is greater than the sum of the squares of the
other two sides, then the triangle is acute.
68. In a 45°-45°-90° triangle, the hypotenuse is
3 times as long as a leg.
69. Opposite side of a parallelogram are congruent.
70. A rectangle is a parallelogram with four right angles.
71. A rhombus is a parallelogram with four congruent sides.
72. The diagonals of a square are congruent.
73. The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
74. Tangents to a circle from apoint are congruent.
75. A central angle of a circle is an angle with its vertex on the circle.
Complete with always, sometimes, or never.
1. Vertical angles are ______________ congruent.
2. Perpendicular lines ______________ form four right angles.
3. A theorem is ______________ a true statement.
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4. A postulate is ______________ proven to be true.
5. Supplements of congruent angles are ______________ congruent.
6. Two angles are ______________ complements.
7. A statement in a proof ______________ has a reason.
8. The diagonals of a quadrilateral ______________ bisect each other.
9. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral
is ______________ a parallelogram.
10. A rectangle ______________ has perpendicular diagonals
11. A square is ______________ a rhombus.
12. A rectangle ______________ has consecutive sides congruent.
13. The diagonals of a trapezoid ______________ bisect each other.
14. A rectangle is ______________ a rhombus.
15. Two lines parallel to a third line are ______________ parallel.
16. An altitude of a triangle is ______________ a median.
17. Opposite angles of a quadrilateral inscribed in a circle are ______________ supplementary.
18. An angle inscribed in a semicircle is ______________ a right angle.
1stSemesterReviewTrueFalse.nb 3
19. A true conditional ______________ has a true converse.
20. A triangle with sides of length è!3!!, 2, and è!7!! is ______________ a right traingle.
21. Vertical angles are ______________ adjacent angles.
22. A conclusion based on inductive reasoning is ______________ correct.
23. Two right triangles with congruent hypotenuses are ______________ congruent.
24. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the
quadrilateral
is ______________ a rhombus.
25. A circle ______________ contains three collinear points.
26. The center of a circle that can be circumscribed about a given triangle is ______________
outside the triangle.
27. The length of a segment is ______________ negative.
28. If point S is between points R and V, then S ______________ lies on RV
õ
.
29. A bisector of a segment is ______________ a line.
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30. A ray ______________ has a midpoint.
31. Congruent segments ______________ have equal lengths.
32. AB
øøö
and BA
øøö
______________ denote the same ray.
33. Three points ______________ determine a plane.
34. Two points ______________ lie in exactly one line.
35. Three points ______________ lie in exactly one line.
36. Three collinear points ______________ lie in exactly one plane.
37. Two planes ______________ intersect.
38. Two intersecting planes ______________ intersect in exactly one point.
39. Two intersecting lines ______________ intersect in exactly one point.
40. Two lines ______________ intersect in exactly one point.
41. Two intersecting lines ______________ lie in exactly one plane.
42. A line and a point not on that line ______________ lie in more than one plane.
43. A line ______________ contains exactly one point.
44. When A and B are in a plane, 
is ______________ in that plane.
AB
45. Vertical angles ______________ have a common vertex.
46. Two right angles are ______________ complementary.
47. Right angles are ______________ vertical angles.
48. Angles A, B, and C are ______________ complementary.
49. Vetical angles ______________ have a common supplement.
50. If a pair of vertical angles are supplementary, the lines forming the angles are
______________ perpendicular.
51. A postulate is ______________ used as a reason in a proof.
52. Supplements of congruent angles are ______________ congruent.
1stSemesterReviewTrueFalse.nb 4
53. Two angles are ______________ complements.
54. A transversal ______________ intersects parallel lines.
55. Skew lines are ______________ coplanar.
56. Coplanar lines are ______________ parallel.
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57. In a plane, two lines perpendicular to a third line are ______________ parallel.
58. Two lines that have no points in common are ______________ parallel.
59. An obtuse angle is ______________ a right angle.
60. A parallelogram is ______________ a quadrilateral.
61. A quadrilateral is ______________ a square.
62. All sides of a parallelogram are ______________ congruent.
63. The diagonals of a quadrilateral ______________ bisect each other.
64. If a conditional is false, then its converse is ______________ false.
65. An angle ______________ has a complement.
66. The diagonals of a trapezoid are ______________ perpendicular.
67. Opposite angles of an inscribed quadrilateral are ______________ congruent.
68. A diameter that bisects a chord is ______________ perpendicualr to the chord.
69. A contrapositive of a true conditional is ______________ true.
70. Two obtuse triangles are ______________ similar.
71. A quadrilateral ______________ has four obtuse angles.
72. Two isoscles right triangles with congruent hypotenuses are ______________ congruent.
73. If the lengths of the sides of two triangles are in proportion, then the corresponding angles
are ______________ congruent.
74. A secant to a circle ______________ contains a chord.
75. The longest chord of a circle is ______________ a diameter.
1stSemesterReviewTrueFalse.nb 5
http://www.frapanthers.com/teachers/zab/Geometry(H)/Reviews/1stSemesterReviewTrueFalse.pdf
CLOSURE
Name five of the nine common words
we learned
_ How far does a line go in each direction? A plane?
_ How many directions does a ray have?
_ What is it called when points are on the same line? In the same plane?
http://ex.susd.org/rchancellor/GeoFiles/
http://ex.susd.org/rchancellor/GeoFiles/
http://mackenziekim.pbworks.com/MCV+4U+-+Calculus+and+Vectors+(Spring+2009)
http://www.doe.k12.ga.us/DMGetDocument.aspx/Released%20Geometry.pdf?p=4BE1EECF99CD364EA55
54055463F1FBBF5D074D5FB1F2CAEB3B63B3ECB220CDD26C2114F3C57D8D230D420D1DC7E9679
&Type=D
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http://rpdp.net/adm/uploads/math/1429GeometryUnit03PracticeTest-ParallelandPerpendicularLines.pdf
http://www.quibblo.com/quiz/9HhKg2d/Geometry-Test-One-Points-Lines-Planes-Angles-and-CongruentFigures
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