Math 3 Review Sheet Ch. 3 November 17

Math 3
Review Sheet Ch. 3
November 17-18, 2011
Before you begin studying for a test, it is impotent to take stock of what you know and what
you need to review. Below I have listed the topics covered during this unit as well as important
topics covered in chapter 2.
Directions: Number each part with a 1, 2 or 3.
• a 1 stands for a topic you still have trouble with or find confusing. These are your first priority.
• a 2 stands for a topic you know, but you may be confused about the details. These are your
second priority.
• a 3 stands for a topic you feel you know well. You could explain this topic to someone else.
These are your third priority.
1. Topics
(a) Congruent Complements and Supplements (Ch. 2)
(b) Addition and Subtraction Properties (Ch. 2)
(c) Multiplication and Division Properties (Ch. 2)
(d) Transitive and Substitution properties (Ch. 2)
(e) Vertical Angles (Ch. 2)
(f) Proving Triangles Congruent (Ch.3 - 3.2)
i. ASA
ii. SAS
iii. SSS
iv. AAS
v. HL-Postulate
(g) CPTCTC
(h) Circles
(i) Altitudes
(j) Medians
(k) Overlapping Triangles
i. Reflexive Property: Angles
, Sides
(l) Definitions and Types of Triangles
i. Scalene
ii. Isosceles
iii. Equilateral
iv. Right
v. Acute
vi. Obtuse
(m) Longest side is across from the largest angle, etc.
(n) Angle ⇒ Sides and Sides ⇒ Angles
Now that you have prioritized the topics you need to focus on, you can more effectively choose
the problems to work on. I have collected a large selection of problems, they range in difficulty.
You should look through the problems and find those relevant to your priorities. You do not
need to complete all the problems, however, you should work on a selection from each level of
difficulty (easy, medium, hard). Do not start with the hardest ones!!!
Easy: 2, 10, 11, 13, 14, 18
Medium: 3, 4, 5, 6, 12, 15, 19
Hard: 7, 9, 16, 17
Very Challenging: 8
Tests are made up of mostly medium problems with some easy problems and some hard problems.
2. What additional information is needed to prove these triangles congruent? What postulate
would you then use to prove triangles congruent? Try to come up with more than one way to
solve this problem.
E
F
A
B
C
D
3. Prove the following: (You may not use the Isosceles Triangle Theorem or its converse)
Given: ∠1 ∼
= ∠2
A
BC ∼
= BC
1
Prove: 4ABC is Isosceles.
B
2
C
4. Prove the following:
Given: 4ADC is isosceles
A
B is the midpoint of AD
B
D
Prove: 4ABC ∼
= 4DBC
C
5. Prove the following:
Given: ∠L is trisected.
L
4F LA is isosceles.
Prove: 4LM F ∼
= 4LOA
M
F
A
O
6. Prove the following:
Given: T is the midpoint of M S
P
Q
∠P M T and ∠QN T are right
∠1 ∼
= ∠2
MR ∼
= SN
Prove: ∠P ∼
= ∠Q
S
R
2
1
M
T
N
7. Prove:
Given: CB ∼
= CD
A
B
∠ABD ∼
= ∠EDB
D
C
CB and CD trisect ∠ACE.
Prove: 4ABE ∼
= 4EDC
E
8. Prove (this one is challenging)
Given: AD ∼
= DB
A
B
AE ∼
= BC
F
H
G
CD ∼
= ED
C
E
Prove: 4AF B is isosceles.
D
9. Prove:
Given: AD ∼
= CF
E
B
∠BAC ∼
= ∠DF E
G
∠ABC ∼
= ∠DEF
A
Prove: 4DGC isosceles
D
C
F
10. Prove:
−−→
Given: F H bisects ∠GF J and ∠GHJ.
G
2
3
1
4
H
F
Prove: F G ∼
= FJ
J
11. Prove:
Given: ∠5 ∼
= ∠6
∠JHG ∼
= ∠O
∼
GH = M O
Prove: ∠J ∼
= ∠P
J
P
5
G
6
H
M
O
12. Prove:
Given: ∠N
∠S
∠N P O
N
S
∠SP R
∠N P O ∼
= ∠SP R
N∼
= SP
Prove: 4N OP ∼
= 4SRP
P
O
R
13.
Given: ∠1
∠2
∠3
∠4
Prove: ∠1 ∼
= ∠4
4
2
1
3
14.
P
Given: P K and JM bisect each other
at R.
M
R
Prove: P J ∼
= MK
J
K
15. Prove: (Do not use the definition of isosceles or the isosceles triangle theorem)
F
Given: JG is an altitude and a median
FJ ∼
= HJ.
G
Prove: 4F JG ∼
= 4HJG
H
J
16.
J
Given: JK ∼
= MK
−→
OP bisects JK and M K
O
Prove: JO ∼
= PK
M
P
K
17. Prove:
Given: HO ∼
= MO
H
M
JO ∼
= KO
O
HJ is an altitude of 4HJK
M K is an altitude of 4M KJ
Prove: ∠M KJ ∼
= ∠HJK
J
K
18.
A
Given: ∠ADB ∼
= ∠ADC
4ABC is isosceles
Prove: AD is a median
B
D
C
19. Prove:
Given: KG ∼
= GJ
∠2 ∼
= ∠4
G
F
H
∠1 is comp to ∠2
∠3 is comp to ∠4
∠F GJ ∼
= ∠HGK
Prove: F G ∼
= HG
3
1
2
K
4
J

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