Download Problem solving geometry - BCMS

Name:
Geometry
Date:
Problem Solving Geometry
June 2011 Assignment
1.
Points M, N, and X are collinear and X is between M and N. If MN = 28 and the ratio between
MX and NX is 3:4, find the length of
.
2.
Point Q is between points P and R on
the value of x.
. If PR = 82, PQ = 4x - 304 and RQ = 4x - 262, find
3.
Ms. Barcenas said, "If you know one vertical angle, you know three other angles." What did she
mean by this?
4.
E is the midpoint of
5.
Isabella was cleaning up a big mess. A forklift operator accidentally dropped a large load of
carpenters' squares (which are actually triangles). They were all over the place. Some were shaped
like equilateral triangles (they were defective), and others were shaped like isosceles triangles. Is
this a good classification system for Isabella to use to begin sorting them back into their proper
piles? Explain. Can you think of a better one?
. If DE = 4x + 10 and EF = 62, find the value of x.
PROBLEM SOLVING GEOMETRY 1
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6.
CD
m
EF
AGC = (3x + 12)
m FHB = (2x + 21)
Find the value of x.
7.
B is in the interior of
If m
m
ADC = (9x - 59) ,
ADB = (2x + 10) ,
and m
BDC = (x + 45) ,
find the value of x.
8.
ADC.
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Name:
Geometry
Date:
Luis and Alyssa were playing a learning game in which they had to virtually sort points, lines, and planes
from a collection of points that appeared on an electronic game board. For a correct response, the board
flashed green. If an incorrect response was given, or if a duplicate of a previous response was offered, the
board would buzz and flash red. Pretend you are playing the game and using the points below. Name 3
points, 3 lines, and 3 planes. Note: The points do not all necessarily lie in the same plane.
9.
As shown in the figure, you can create a pyramid by folding sides of a piece of paper up and then use
masking tape to hold it together. Of the five planes containing sides of the pyramid, which two planes do
not intersect?
A.
B.
C.
D.
E.
1 and 4
1 and 5
2 and 5
2 and 4
All planes intersect.
PROBLEM SOLVING GEOMETRY 3
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10. Why are points, lines, and planes considered fundamental objects in geometry?
11. Is it possible for a bisector to divide a line into unequal parts? Explain.
12. Suppose M is between L and N. LM = (2 1/2y + 3), MN = (2y + 7/2), LN = 123. Find the value of y.
13. Find a set of objects in the room such that each set contains something represented by one point, one
line, and one plane. How many such sets are there?
14. In the figure,
and m
Find m
,
,
DBC=26 .
ABE.
15. A triangle is the figure formed by the union of three segments determined by ___________.
A.
B.
C.
D.
E.
F.
three skew points
three angels
three collinear points
any three points
three noncollinear points
three rays
16. Find the distance between the two points.
Name:
Geometry
Date:
(a) G(5, 8), H(6, -7)
(b) M(5, -8), N(-3, 3)
(c) P(-1, 1), Q(-7, -8)
17. E is the midpoint of
.
If DE = 3x + 9 and EF = 6x - 6,
then DF = ______.
18. If m
UVW = m
XYZ, then ______.
Points U, V, W, X, Y, and Z are coplanar.
UVW and
UVW
UVW and
XYZ form a straight angle.
XYZ
XYZ are adjacent angles.
19. The distance between two points is the ___________ of the ___________ joining the points.
A.
B.
C.
D.
E.
measure, complementary angle
length, segment
length, ray
measure, supplementary angle
radius, circle
20. Two angles are complements. 34
Find the measures of the two angles.
less than twice the larger angle equals twice the smaller angle.
21. If Ms. Cordova cuts a cake into slices (through the center of the cake) that have a vertex angle of
20°, how many such whole slices can be made from half a cake?
22. Which of the following statements is NOT true?
PROBLEM SOLVING GEOMETRY 5
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A. Planes X and Y contain both M and N.
B. Plane Y and
intersect in point L.
C. Points L, M, N, and P are coplanar.
D. Points N and P are noncoplanar.
23.
Line AB is a transversal of line CD and line EF.
Circle which of the following is true?
BHE is the supplement of
EHG is the supplement of
DGA is the supplement of
DGA is the complement of
DGA
DGH
FHB
EHG
None of the above
24.
How many endpoints are required to define the locations of 7 different rays and 5 different lines
such that no rays or lines share any common point with any other rays or lines?
Name:
Geometry
Date:
25.
Is it possible for two angles located on different parts of the surface of the earth to be
complementary? Explain.
PROBLEM SOLVING GEOMETRY 7
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Name:
Geometry
Date:
PROBLEM SOLVING GEOMETRY 9