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© 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 mA mB . Two angles A and B are supplementary to each other if mA mB 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 1 © 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 . 2 © 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) 3