Geometry
Chapter 2 Review Olympics
• One sheet per player
• Make an answer column on the left side of
your paper
• Work together to solve each question
• Winning team earns a reward
• We will go over the process and answers for
each
1) True or False.
2
a) Perp. Lines form congruent adj. angles.
b) A reason that can be used in to justify a statement is
tomorrow’s theorem.
c) If 2 angles are comp.’s of the same angle, then the angles
are comp.’s of each other.
2) True or False.
a) Two right angles are supplementary.
b) A statement that contains “if and only if” is called a
biconditional.
c) Right angles can be vertical angles.
2
3) Name the defn., prop., post., or thm.
that justifies each statement.
a) Angle P is congruent to angle P.
b) If 2x + y = 70 and y = 3x, then 2x + 3x = 70.
c) If AB = CD, CD = EF, then AB = EF.
1
4) Name the defn., prop., post., or thm.
that justifies each statement.
1
a) m<AOD = m<AOC + m<3
b) If ray OB bisects <AOC then m<1 = (1/2)m<AOC.
A
B
C
1
2
3
O
D
5) Name the defn., prop., post., or thm.
that justifies each statement.
2
a) m<5 = m<6
b) If m<4 + m<6 = 90, then <4 and <6 are complementary.
c) m<5 + m<7 = 180
d) If line KL and ray BM are perp., then m<8 = 90.
M
4
K
8
6
5 7
B
L
6) The supplement of an angle is 21 less
than twice the angle. Find the angle and
the supplement.
2
7) You are given that line BF and line HD
are perp., m< GIB = 120, and m< EID = 60.
Complete each with a numerical answer.
3
m<AID
m<CID
m<GIE
A supplement of <HIG has a measure of _____
B
A
C
H
I
D
G
E
F
8) If <Q and <R are supp., find x, then
find the m<Q and m<R.
m<Q = x + 16
m<R = 2x – 16
1
9) Ray SW bisects <RST and m<RST = 72.
Ray SZ bisects <RSW. Find m<ZST.
2
10) Given: Ray BD bisects <ABE
Prove: m<2 = m<4
3
A
B
D
1
2
3
4
E
• Rows 1 and 2 Trade Papers
• Rows 3 and 4 Trade Papers
• Rows 5 and 6 Trade Papers
• Score only one sheet, then add it to their
teammate’s score.
• Points: Gold = 3 Silver = 2 Bronze = 1
• If there is more than 1 part, all parts must be
correct to get the points
Answer
1) True or False.
2
a) Perp. Lines form congruent adj. angles.
Answer: True
b) A reason that can be used in to justify a statement is
tomorrow’s theorem.
Answer: False
c) If 2 angles are comp.’s of the same angle, then the angles
are comp.’s of each other.
Answer: False
Answer
2) True or False.
2
a) Two right angles are supplementary.
Answer: True
b) A statement that contains “if and only if” is called a
biconditional.
Answer: True
c) Right angles can be vertical angles.
Answer: True
Answer
3) Name the defn., prop., post., or thm.
that justifies each statement.
a) Angle P is congruent to angle P.
Answer: Reflexive POE
b) If 2x + y = 70 and y = 3x, then 2x + 3x = 70.
Answer: Subst. POE
c) If AB = CD, CD = EF, then AB = EF.
Answer: Trans. POE
1
Answer
4) Name the defn., prop., post., or thm.
that justifies each statement.
1
a) m<AOD = m<AOC + m<3
Answer: < Add. Post.
b) If ray OB bisects <AOC then m<1 = (1/2)m<AOC.
Answer: < Bis. Thm.
A
B
C
1
2
3
O
D
Answer
5) Name the defn., prop., post., or thm.
that justifies each statement.
2
a) m<5 = m<6
Answer: Vert. <‘s congruent or thm.
b) If m<4 + m<6 = 90, then <4 and <6 are complementary.
Answer: Comp <‘s Defn.
c) m<5 + m<7 = 180
Answer: < Add. Post.
d) If line KL and ray BM are perp., then m<8 = 90.
M
Answer: Perp. Line Defn
4
K
8
6
5 7
B
L
Answer
6) The supplement of an angle is 21 less
than twice the angle. Find the angle and
the supplement.
2
Process: 180 – x = 2x – 21
Answer: Angle = 67 Supp = 113
Answer
7) You are given that line BF and line HD
3
are perp., m< GIB = 120, and m< EID = 60.
Complete each with a numerical answer.
Answer: 120
a) m<AID
b) m<CID Answer: 30
c) m<GIE
Answer: 90
Answer: 150
d) A supplement of <HIG has a measure of _____
B
A
C
E
I
D
G
E
F
Answer
8) If <Q and <R are supp., find x, then
find the m<Q and m<R.
m<Q = x + 16
Process:
1
m<R = 2x – 16
x + 16 + 2x – 16 = 180
Answer: x = 60, m<Q = 76, m<R = 104
Answer
9) Ray SW bisects <RST and m<RST = 72.
Ray SZ bisects <RSW. Find m<ZST.
Process:
See Board.
Answer: 54
2
Answer
10) Given: Ray BD bisects <ABE
Prove: m<2 = m<4
Statements
Reasons
1) Ray BD bisects <ABE
1) Given
2) m<1 = m<2
2) < bis. Defn.
3) m<4 = m<1
3) Vert <‘s cong. (thm.).
4) m<2 = m<4
4) Trans. (Subst.)
3
A
B
D
1
2
3
4
E
Tiebreaker) An angle is 10 more than
3 times its complement. Find the angle.
Answer: 70
HW
• P. 67-68 #1-20 P. 69 # 12 Proof
• Winners do Odds
• Test Tomorrow
• $1