unit 1 – introduction to geometry and reasoning
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Unit 1 – Introduction to Geometry and Reasoning. Review for Final Exam. True/False. The three basic building blocks of geometry are point, line, plane. True/False. The ray through point P from point Q is written in symbolic form as. True/False. The vertex of angle PDQ is point P. - PowerPoint PPT PresentationTRANSCRIPT
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Unit 1 – Introduction to Geometry and ReasoningReview for Final Exam
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True/False
•The three basic building blocks of geometry are point, line, plane.
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True/False
•The ray through point P from point Q is written in symbolic form as .PQ
uuur
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True/False
•The vertex of angle PDQ is point P.
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True/False
•The symbol for perpendicular to is .
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True/False
•An acute angle is an angle whose measure is more than 90°.
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True/False
•If intersects at point P, then and are a pair of vertical angles.
ABsuur
CDsuur
APDAPC
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True/False
•If the sum of the measure of two angles is 180°, then the two angles are complementary.
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True/False
•If two lines are parallel to the same line, then they are parallel to each other.
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True/False
•If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
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True/False
•If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the segment.
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True/False
•If the sum of the measure of two angles is 180°, the two angles are vertical angles.
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True/False
•Inductive reasoning is the process of showing that certain statements follow logically from accepted truths.
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True/False
•In a geometric construction, you use a protractor and a ruler.
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Find the next number in the sequence, and describe the pattern.
•100, 97, 91, 82, 70, ____
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Find the next number in the sequence, and describe the pattern.
•3, 5, 8, 12, 17, ______
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Number Patterns
•If at a party there are a total of 741 handshakes and each person shakes hands with everyone else at the party exactly once, how many people are at the party?
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Number Patterns
•If 28 lines are drawn on a plane, what is the maximum number of points of intersection possible?
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Number Patterns
•If a whole bunch of lines (no two parallel, no three concurrent) intersect in a plane 2926 times, how many lines are a whole bunch?
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Number Patterns
•If in a 54-sided polygon, all possible diagonals are drawn from one vertex, they divide the interior of the polygon into how many regions?
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Number Patterns
•How many sides does the polygon have if all possible diagonals drawn from one vertex divide the interior of the polygon into 54 regions?
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Find the nth term
n 1 2 3 4 5 6 … nf(n) -7 -2 3 8 13 18 …
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Find the nth term
n 1 2 3 4 5 6 … nf(n) -1 2 7 14 23 34 …
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Find the pattern to finish the statement…
•The sum of the first 30 positive odd whole numbers is __________.
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Find the pattern to finish the statement…
•The sum of the first 30 positive even whole numbers is __________.
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Given : ,corresponding angles congruent
Prove : 4 6 (alternate interior angles congruent)
(you may not use the parallel lines conjecture in this proof)
m n
Ð @Ð
P
1 24 3
67
5
8
m
n
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Given : 4, 5 are supplementary
Prove :m n
Ð Ð
P
1 24 3
67
5
8
m
n