Download Test on Elementary Geometry and Mathematical Structure

© 2014 Michael Tung
G8 Elementary Geometry and Math Structure Test
1. True or False. (2 marks each)
a. An Undefined Concept is a fundamental concept its meaning is accepted without
definition.
b. A Geometric Point has no length, width or thickness, it merely indicates a place or
position.
c. A Line is an infinite set of points which extends endlessly in both directions.
d. A Plane is a set of points that forms a completely flat surface extending
indefinitely in all directions.
e. Two or more points are Collinear if they lie on a same straight line.
f.
g.
h.
i.
j.

AB represents a line segment with endpoints A and B.
Two or more Line segments can be equal.
Two or more Line segments can be Congruent.
Two angles A and B are complementary to each other if mA  mB .
Two angles A and B are supplementary to each other if mA  mB  180 .
2. Fill in the blanks with the words “always”, “sometimes” or “never”. (4 marks each)
a. The complement of an angle is ＿＿＿＿＿ an acute angle.
b. The supplement of an angle is ＿＿＿＿_ an obtuse angle.
c. The supplement of a right angle is ＿＿＿＿＿ a right angle.
d. The complement of an angle is ＿＿＿＿＿ an obtuse angle.
e. The supplement of an angle is ＿＿＿＿＿ congruent to the complement of an the
angle.
3. Multiple Choices Questions. (3 marks each)
a. The supplement of the complement of an acute angle is always
i. An Acute angle
ii. An Obtuse angle
iii. A Straight angle
iv. A Right angle
b. Two angles that are both congruent and supplementary must be
i. Adjacent angles
ii. Acute angles
iii. Right angles
iv. Complementary
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© 2014 Michael Tung
c. If an Acute angle varies so that its measure increases, the measure of its
supplement
i. Increases
ii. Decreases
iii. Remains the same
d. If an acute angle varies so that its measure decreases, the measure of its
complement
i. Increases
ii. Decreases
iii. Remains the same
e. The difference between the measure of the supplement and the measure of the
complement of an angle is the measure of
i. An Acute angle
ii. A Right angle
iii. An Obtuse angle
iv. A Straight angle
f. If two adjacent angles have their noncommon sides in the same straight line, they
are always
i. Congruent
ii. Complementary
iii. Supplementary
iv. Vertical
____
____
4. In the diagram BD  AC . (5 marks each)
B
C
D
A
a. Name two congruent adjacent angles.
b. State the degree measure of BDA .
_____
c. Name the point that is the foot of the perpendicular from B to AC .
_____
d. Name the line segment whose length measures the distance from B to AC .
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© 2014 Michael Tung
5. Consider the Mathematical Structure (  0, 1, 2, 3 ,   4
 4 is defined as:
 a  b , if a  b  4
For any a  4 b  
 a  b - 4 , if a  b  4
 ) , where the Binary Operation
For example, since 0  1  1  4 , so 0  4 1  0  1  1 .
and since 2  3  5  4 , so 2  4 3  2  3 - 4  1
and since 2  2  4  4 , so 2  4 2  2  2 - 4  0
4
0
1
2
3
0
1
1
2
3
0
1
a. Complete the above Cayley Table. (13 marks)
b. Is (  0, 1, 2, 3 ,   4
 ) closed? (1 mark)
c. State the Associative property for this Structure? (3 marks)
d. What is the Identity of this Structure? (1 mark)
e. What is the Inverse of each element? (4 marks)
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