Download 1st sem geometry final

G.1.F Geometry Terms
Name ______________________________
In the table below, fill in the information about each term listed
Term
Undefined Term
Definitions
Postulates
Theorems
Example
Distinguishing feature
How it’s Used
G.2.B Angles formed by parallel lines
c
p
b
q
(1)
3
2
4
5
6
a
r
9
10
7
11
12
8
21
17
13
23
19
22
18
14
24
15
20
29
16
31
25
26
30
27
32
28
33
34
35
(36)
Refer to the diagram above.
Given that a ‖ b ‖ c and p ‖ q ‖ r,
Use each of the four angle relationships at least once to prove angle 1 is congruent to angle 36.
Statement
Reason
G.2.C Constructions
Given line segment AB
1. Construct the perpendicular bisector of AB. Label the bisecting line n and intersection point (midpoint) C.
2. From point C, extend the bisecting line n.
3. Make a point D on line n so that AC ≅ CD.
3. Construct a line m perpendicular to CD thru point D.
A
B
G.2.D Lines and planes
1. List three undefined terms:
2. Give 2 examples of the intersection of 3 lines in a plane with pictures and words.
Ex1
Ex2
3. Give 2 examples of the intersection of 3 lines in space with pictures and words.
Ex1
Ex2
4. Give 2 examples of the intersection of 3 planes in space with pictures and words.
Ex1
Ex2
5. Give 2 examples of the intersection of 2 lines & a plane in space with pictures and words.
Ex1
Ex2
1. Label each example as Inductive or Deductive
G.1.A Logic
a. Dogs are mammals. Mammals have kidneys. Therefor dogs have kidneys.
b. Jeremiah talked to the neighbor Tom. Tom said it was his daughter’s birthday. Jeremiah watched a
bunch of people show up at the neighbor’s house. He concluded they must be having a party for their
daughter.
c. Harmonie always goes out on Friday night. When Harmonie goes out she always wears red heals.
Tonight is Friday night. Tonight Harmonie will wear red heals.
2. Determine whether or not the last shape in the sequence fits. If yes, state why. If no, state why not and draw
the shape that would work better
3. For the given statement, write out each of the following:
Statement: If you don’t sleep enough, then your grades will suffer.
a. Hypothesis:
b. Conclusion:
c. Converse:
(If converse is false, state a counter example)
d. Inverse:
(If inverse is false, state a counter example)
e. Contrapositive:
(If contrapositive is false, state a counter example)
G.1.C.2.A Deductive Reasoning, Proving Lines Parallel
Write a two column proof for the following:
1
Given:
2 and
3 are supplementary angles
m
2
Prove: m ‖ n
3
Statement
n
Reason
1
Given:
2 and
3 are supplementary angles
m
2
Prove: m ‖ n
n
3
Statement
Reason
G.3.A Basic triangle postulates
Find each of the missing angle measures
76°
9°
80°
x
x
z
x
y
140°
x
63°
List sides shortest to longest
85°
x
z
33°
y
List angles biggest to smallest
a
45°
6
y
x
b
70°
7
8
65°
z
c
Given two side lengths, find a third side that would make a triangle. Show work.
2,3, ?
5,7, ?
G.3.B SSS, SAS, ASA, AAS
Pick and choose any TWO proofs to solve.
Given: BD bisects < ABC
Given: AB ┴ CM
AB ┴ DB
<A=<C
Prove: ∆ ABD = ∆ CBD
M is the midpoint of AB
A
< BMD = < MAC
Prove: ∆ AMC = ∆ MBD
B
D
A
C
C
M
D
B
Given: HK = LG
Given: VY bisects WX
HF = LJ
WX bisects VY
FG = JK
Prove: ∆ VZW = ∆ YZX
V
Prove: ∆ FGH = ∆ JKL
W
F
Z
X
H
Y
R
K
G
J
L
G.3.D Pythagorean Theorem
For each right triangle, find the missing side indicated. Show all necessary work.
X
12
7
8
6
X
Determine if the numbers given create a Pythagorean triple. Show your work.
a) 12,16,20
b) 4,6,7
Draw a picture and solve the following word problem.
If my dog runs 2 miles north, then 5 miles west; how far is he from where he started?
G.3.C
Special Rt. triangles
For each right triangle, find the missing side indicated. Show all necessary work.
8
Y
10
45°
45°
Z
W
12
V
11
60°
60°
60°
U
4
Find the missing length indicated. Show all work.
30°
T
16
45°
S
16
60°
G.3.E Trig. Ratios
Solve for the unknowns below using trigonometric ratios
x
b
35
c
q
X
17
25
76
8
47°
y
z
28
1. Tan x =
r
x°
p
a
2. Side X =
3. Angle X =
Solve the following story problems
7. A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes
an angle of 58° with the ground. Find the length of the wire.
8. A ladder leaning against a wall makes an angle of 74° with the ground. If the foot of the ladder is 6.5 feet
from the wall, how high on the wall does the ladder reach?
G.3.G Polygons
1. a. What is the sum of the measure of the interior angles of a dodecagon?
b. What is the measure of a single interior and exterior angle?
2. If a regular polygon has 22 sides, what would the measure of an exterior angle be?
3. (Create a table to) Derive the formula for the sum of the interior angles of any regular polygon. Must use
the following convex polygons in your derivation: triangle, quadrilateral, pentagon, hexagon and n-gon.
4. Name each shape shown, and state the relationship between the angles indicated.
If possible find angle a. (assume regular polygon)
a
b
a
a
b
b
b
a
b
a
G.3.F Parallelograms
1. Solve for the unknowns in parallelograms EFGH and PQRS below
P
Q
3y - 5
E
F
2x + 5
4x - 15
G
4x - 15
H
S
R
2y + 15
2. Mark which property is true for each figure in the table below
Property
The diagonals form congruent triangles
Consecutive angles are supplementary
Both pairs of opposite sides are parallel
Opposite sides are congruent
All sides are congruent
Diagonals bisect each other
Angles are 90°
Opposite angles are congruent
All angels are congruent
Diagonals are perpendicular
The diagonals are congruent
Parallelogram
3.
Rhombus
Rectangle
A
Given:
AB ‖ CD, AC ‖ BD
Prove:
AB = CD, AC = BD
C
Statement
a. AB ‖ CD, AC ‖ BD
b. < BAD = < CDA
c. < BDA = < CAD
d. AD = AD
e. ∆ ADB = ∆ CAD
f. AB = CD
g. AC = BD
B
D
Reason
Square