Download Review for Quiz#2 Answers

Geometry Quiz #2 Review
Name_______________________
These are only sample questions, but hopefully they will help!
1. Draw a figure with 5 labeled points so that:
A, B, and C lie on DE. AB U AC = BC and AC ∩ AD = AC
2. What is the complement of (40 + x)˚?_____________
3. Find the measures of R, S and Q if R is supplementary to S, R is complementary to Q
and mR = x˚, mQ = (x + 30)˚.
4. Use the figure to the right for the next questions:
A
AB  CG and EF  DH
D
A) If mACD = 20˚, then mBCD = _________
F
C
E
G
B) If ACD  FEG and mDCE = 65˚,
find mGEH. _________
C) If mACD = (2x – 30)˚ and mDCE = (x + 45)˚
H
B
Find x_______ and mDCE. _________
D) If mCED = (2x – 30)˚ and mDEG = (x + 45)˚
Find x_______ and mDEG._________
E) If mCED = (2x – 30)˚ and mHEG = (x + 45)˚
Find x_______ and mHEG._________
F) If mDEC = 2x + y, mCEH = y – 10 and mHEG = 3x – 5, find x_______, y = ________
And mGED.___________
5. An angle and its supplement are in the ratio: 3:7. Find the measure of the smaller angles
complement.
6. Write the reasons for the following algebraic proof:
1. 4x + 8 = 20
1. Given
2. 4x + 8 – 8 = 20 – 8
2. ______________________
3. 4x + 0 = 20 – 8
*3. ______________________
4. 4x = 20 – 8
*4._______________________
5. 4x = 12
5._______________________
6. ¼(4x) = ¼(12)
6._______________________
7. (¼·4)x = ¼(12)
7. _______________________
8. 1·x = ¼(12)
*8._______________________
9. x = ¼(12)
*9._______________________
10. x = 3
10._______________________
7. Given: AIK  BEK,  AIT  BET
K
Prove: KIT  KET
A
I
E
B
T
8. If the complement of the supplement of an angle is 70˚ less than the measure of the angle, find
the measure of the angle.
9. Complete the “given, statement, reason” chart below:
A
O
A
O
B
1 2
2
1  3
3
3
C
D
OA OD
C
D
Geometry Quiz #2 Review
Name_______________________
These are only sample questions, but hopefully they will help!
1. Draw a figure with 5 labeled points so that:
A, B, and C lie on DE. AB U AC = BC and AC ∩ AD = AC
D
C
A
B
E
2. What is the complement of (40 + x)˚? 90 – (40 + x) = (50 – x)˚
3. Find the measures of R, S and Q if R is supplementary to S, R is complementary to Q
and mR = x˚, mQ = (x + 30)˚. mR = 30˚, mQ = 60˚, mS = 150˚
4. Use the figure to the right for the next questions:
A
AB  CG and EF  DH
D
A) If mACD = 20˚, then mBCD = __160˚___
F
C
E
G
B) If ACD  FEG and mDCE = 65˚,
find mGEH. ___65˚______
C) If mACD = (2x – 30)˚ and mDCE = (x + 45)˚
H
B
Find x__25___ and mDCE. _70˚____
D) If mCED = (2x – 30)˚ and mDEG = (x + 45)˚
Find x__55___ and mDEG.__100˚__
E) If mCED = (2x – 30)˚ and mHEG = (x + 45)˚
Find x___75__ and mHEG._120˚___
F) If mDEC = 2x + y, mCEH = y – 10 and mHEG = 3x – 5, find x__50_, y = _45____
And mGED.___35˚____
5. An angle and its supplement are in the ratio: 3:7. Find the measure of the smaller angles
complement.
3k + 7k = 180  10k = 180  k = 18 so the smaller angle is 54˚ and its complement is 36˚.
6. Write the reasons for the following algebraic proof:
1. 4x + 8 = 20
1. Given
2. 4x + 8 – 8 = 20 – 8
2. Additive Property of Equality
3. 4x + 0 = 20 – 8
*3. Additive Inverse Property
4. 4x = 20 – 8
*4. Additive Identity Property
5. 4x = 12
5. Simplification
6. ¼(4x) = ¼(12)
6. Multiplicative Property of Equality
7. (¼·4)x = ¼(12)
7. Associative Property of Multiplication
8. 1·x = ¼(12)
*8. Multiplicative Inverse Property
9. x = ¼(12)
*9. Multiplicative Identity Property
10. x = 3
10. Simplification
7. Given: AIK  BEK,  AIT  BET
K
Prove: KIT  KET
1. AIK  BEK,  AIT  BET
1. Given
2. AIK and KIE are supp.
2. Linear pairs
AIT and TIE are supp.
BEK and KEI are supp.
BET and TEI are supp.
3. KIE  KEI, TIE  TEI
4. KIT  KET
are
supplementary.
A
3. Supplements
of  angles are .
4.  angles + 
I
E
B
T
angles   angles.
8. If the complement of the supplement of an angle is 70˚ less than twice the measure of the
angle, find the measure of the angle.
90 – (180 – x) = x – 70  90 – 180 + x = 2x – 70  -90 + x = 2x – 70  -90 = - 70 this
is impossible! 
9. Complete the “given, statement, reason” chart below:
A
O
A
O
B
1 2
2
1  3
C
3
D
OA OD
C
3
D
AOC  BOD
2 and 3 are complementary
 angles +  angles   angles
Perpendicular pairs are
complementary.