Download Homework on Building Blocks of Geometry

Geometry 1
Name:
Worksheet: Building Blocks
1.
In geometry, what do you call statements that are accepted as true without proof?
2.
In geometry, what do you call statements that can be proved?
3.
Which of the following statements is generally accepted by most people to be true?
4.
a.
Most high school classes are difficult.
b.
Most high school students spend 3 hours a day on homework.
c.
The goal of high school is to teach students.
d.
All students enjoy going to school.
Which of the following are postulates of geometry (more than one)?
a. The diagonals of a square are perpendicular.
b. If a plane contains two points of a line, then that plane contains the whole line.
c. If a line intersects a plane that does not contain it, then it intersects the plane in
exactly one point.
d. Every line contains at least two points.
e. A rectangle is a closed, 4-sided figure containing 4 right angles.
5.
What geometric object is the intersection of two lines?
6.
What geometric object is the intersection of two planes?
7.
How many planes can contain two intersecting lines?
8.
What geometric object is the intersection of a line and a plane?
9.
Consider the postulate: Two points determine a line.
This means that if you are given any two points, then there is one and only one line that contains
them. From this it follows that two lines cannot intersect in more than one point, because
otherwise you would have two points that are contained in two different lines.
Should the statement, “two lines intersect in at most one point” be classified as a postulate or a
theorem ?
Why?
10. Refer to this diagram of six coplanar points:
E
A
D
F
C
B
a. Are points A and C collinear?
b.
Are points A, D and F collinear?
c. Name all points (other than B and C) which are collinear with B and C.
d. Name three points that are noncollinear.
11.
Two of the postulates of geometry are:
P2: Every line contains at least two points.
P7b: Any three noncollinear points lie in exactly one plane.
Use these two postulates to prove the following:
Theorem: There is exactly one plane containing a given line and point not on the line.
12.
B
Refer to the following rectangular box:
C
A
D
F
G
E
H
a. Are points E, H and D coplanar?
b. Are points E, H and B coplanar?
c. Are points A, B, E and F coplanar?
d. Are points A, F and G coplanar?
e. Are points A, F, G and D coplanar?
f. Are points B, E, H and D coplanar?
g. Name a 4th point that is coplanar with points B, E and H.
h. Name a 4th point that is coplanar with points A, C and G.
13.
Consider the following figure consisting of 4 coplanar points:
.
.
.
B
A
C
.
D
Which of the following can NOT be true (there is only one)?
a. AB + AD = BD
14.
b. AC + AD = BD
c. AC = DC
d. BC + CD = BD
In which case below is it true that ACE and ACD are adjacent angles? (Only one answer.)
A
(a)
A
(b)
D
C
C
D
E
E
D
E
C
C
E
A
(d)
D
A
(c)
A
(e)
C
E
D
15.
If P is the midpoint of MN and NP = 5, then which TWO of the following are true?
(a) MN = 5
16.
17.
(d) MP = 10
Suppose C, D and E are collinear, CD = 5 and CE = 8. Then which ONE of the following can
NOT be true?
b. DE = 3
c. DE = 13
Suppose F, G and H are three points which may or may not be collinear, FG = 7 and FH = 9.
Then which ONE of the following can NOT be true?
a. GH = 3
19.
(c) MN = 10
Suppose A, B and C are collinear with B between A and C. If AB = 12 and AC = 15,
then BC = ?
a. DE = 11
18.
(b) MP = 5
b. GH = 15
c. GH = 17
d. GH = 2

Suppose GH bisects KGP and KGH measures 80 . Then what is the measure of KGP ?
20. Suppose QRT and QRS are adjacent angles, QRT measures 20 , and SRT measures
80 . Then what is the measure of QRS ?