Download Wandering thru Caves

Still Wandering through Caves
Welcome back, young adventurer. After wandering through Lord Flathead IV’s Great
Underground Empire, you have discovered the following pieces of information.
A)
B)
C)
D)
E)
F)
G)
H)
Cavern
Cavern
Cavern
Cavern
Cavern
Cavern
Cavern
Cavern
1 connects to caverns 2, 5, 6, 7.
2 connects to caverns 1, 14, 6.
4 connects to caverns 3, 9, 10, 15.
8 connects to caverns 3, 11.
9 connects to caverns 4, 5.
10 connects to caverns 3, 4.
12 connects to caverns 11, 13.
13 leads to freedom.
Given: Now, you find yourself at a dead end in Cavern 14.
Goal: Leave Lord Flathead’s domain.
Instructions:
Find a path from Cavern 14 to freedom and justify how you are able
to move from one cavern to the next using the connections you have
discovered during your recent wanderings.
Location
Justification
Cavern 14
Given
Given: When you enter Cavern 8, you discover a golden torch hidden in a deep well.
Unfortunately, you left your rope in a dead end cavern that emptied into the
only cavern with four exits.
Goal:
Find your way back from Cavern 8 to the proper cavern to fetch your rope so
that you will be able to retrieve the golden torch from the well, again justifying
how you are able to move from one cavern to the next using the connections
you have discovered during your recent wanderings.
Location
Justification
Cavern 8
Given
Still Wandering through Geometry
From your informal investigations into geometry thus far, you have discovered the following
geometric tools (among others).
A)
B)
C)
D)
E)
F)
G)
H)
I)
J)
K)
L)
M)
N)
O)
P)
Q)
R)
S)
T)
The Definition of a Right Angle
The Definition of Perpendicular Lines
The Definition of a Midpoint
The Definition of an Angle Bisector
The Definition of Linear Pair
The Definition of Vertical Angles
The Definition of Complementary Angles
The Definition of Supplementary Angles
Transitive Property
Substitution Property
Addition Property
Subtraction Property
Reflexive Property
Distributive Property
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Postulate
Congruent Complements Theorem
Congruent Supplements Theorem
Vertical Angles are congruent.
U)
V)
W)
Perpendicular lines intersect to form four right angles
All right angles are congruent
If exterior sides of two adjacent angles are , then the
angles are complementary.
X) If two lines are parallel, then the corresponding angles
are congruent.
Y) If two lines are parallel, then the alternate interior
angles are congruent.
Z) If two lines are parallel, then the alternate exterior
angles are congruent.
AA) If two lines are parallel, then the same side interior
angles are congruent.
BB) The sum of the angles of a triangle equals 180°.
CC) Third Angle Theorem
DD) Side-Side-Side Postulate
EE) Side-Angle-Side Postulate
FF) Angle-Side-Angle Postulate
GG) Angle-Angle-Side Theorem
HH) Hypotenuse-Leg Theorem
CPCTC Corresponding Parts of  s are 
Show that the following geometric propositions are true using the given information and the
logical tools listed above.
P
O
I
N
T
Given: I is the midpoint of PT
O is the midpoint of PI
N is the midpoint of IT
Show That: PO = NT
Geometric Statement
Justification
N
B
Given:  BAG and  TAG are complementary
AB is the angle bisector of NAG
Show That:  BAN and  TAG are complementary
Geometric Statement
G
A
Justification
T
Given: 2  4; AC = AF
Prove: CAB  FAD
D
Geometric Statement
Justification
Geometric Statement
Justification
Geometric Statement
Justification
B
E
5
C
6
1
2
3
4
F
A
Given: 2  4; EC = EF
Prove: CED  FEB
D
B
E
5
C
6
1
2
3
4
F
A
Given: 2  1; GO = TO
Prove: HOT  HOG
Then Prove: 3  6
O
12
3
G
4
5
H
6
T
Given: HO  GT; GH  TH
Prove: HOT  HOG
Geometric Statement
Justification
Geometric Statement
Justification
Geometric Statement
Justification
Then Prove: GO  TO
O
12
3
4
G
5
6
H
T
Given: HE = MO ; HO = ME
Prove: HOM  MEH
Then Prove: 1  4 ; 2  3
H
O
2
1
4
3
E
M
Given: HE║MO ; HO║ME
Prove: HOM  MEH
Then Prove: HE  MO ; HO  ME
H
O
2
1
4
3
E
M