Unit 1 – Introduction to Geometry and ReasoningReview 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 .PQ

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True/False

•The vertex of angle PDQ is point P.

True/False

•The symbol for perpendicular to is .

True/False

•An acute angle is an angle whose measure is more than 90°.

True/False

•If intersects at point P, then and are a pair of vertical angles.

ABsuur

CDsuur

APDAPC

True/False

•If the sum of the measure of two angles is 180°, then the two angles are complementary.

True/False

•If two lines are parallel to the same line, then they are parallel to each other.

True/False

•If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

True/False

•If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the segment.

True/False

•If the sum of the measure of two angles is 180°, the two angles are vertical angles.

True/False

•Inductive reasoning is the process of showing that certain statements follow logically from accepted truths.

True/False

•In a geometric construction, you use a protractor and a ruler.

Find the next number in the sequence, and describe the pattern.

•100, 97, 91, 82, 70, ____

Find the next number in the sequence, and describe the pattern.

•3, 5, 8, 12, 17, ______

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?

Number Patterns

•If 28 lines are drawn on a plane, what is the maximum number of points of intersection possible?

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?

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?

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?

Find the nth term

n 1 2 3 4 5 6 … nf(n) -7 -2 3 8 13 18 …

Find the nth term

n 1 2 3 4 5 6 … nf(n) -1 2 7 14 23 34 …

Find the pattern to finish the statement…

•The sum of the first 30 positive odd whole numbers is __________.

Find the pattern to finish the statement…

•The sum of the first 30 positive even whole numbers is __________.

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

Given : 4, 5 are supplementary

Prove :m n

Ð Ð

P

1 24 3

67

5

8

m

n