Download Chapter 2 Test Review Key

Geometry Chapter 2 Practice Test
1) Given: 4x+5=-3
=6x
Prove: x=4
Statement
Justification
1)
4x+5=-3
Given
2)
=6x
Given
3)
4x+5=6x-3
Substitution Prop of =
4)
5=2x-3
Subtraction Prop of =
5)
8=2x
Addition Prop of =
6)
x=4
Division Prop of =
2) Justify each step of the equation.
Given: AC=21
2y
A
1)
AB+BC=AC
Segment Addition Postulate
2)
2y+(3y-9)=21
Substitution Prop of =
3)
5y-9=21
Simplify
4)
5y=30
Addition Prop of =
5)
y=6
Division Prop of =
3y-9
B
C
3) Assume the following are true.
 If Dan does not buy ice cream, then he did not shop.
 If Julie buys pizza, then she will have some left over.
 If the store is open, then Dan and Julie will shop.
 If Julie shops, then she will buy pizza.
 The store is open.
a) Did Julie buy ice cream?
Not necessarily so No
c) Did Dan eat some of Julie’s pizza?
Not necessarily so No
b) Did Julie have pizza left over?
Yes
d) Did Dan buy ice cream?
Yes
4) Write the following as conditional statements. If possible, use a biconditional.
a) The month that follows April is called May.
The month is April if and only if it follows May.
b) Billy rocks out when he listens to opera.
If Billy is listening to opera, then he is rocking out.
c) Two angles that measure 28 and 62 degrees are complements.
If two angles measure 28 and 62 degrees, then they are complements.
5) A. If I tell Rover to “play dead,” then he will lay on his back.
B. If Rover gets put out to his doghouse, then he did not lay on his back.
a) Write the contrapositive of statement B.
If I tell Rover to lay on his back, then he does not get put in the
doghouse.
b) Suppose I tell Rover to play dead. Using the law of syllogism, what can you
conclude from these statements?
He does not get put in the doghouse.
c) Suppose Rover gets put out to the doghouse. Again, using the law of syllogism,
what can you conclude?
I did not tell him to play dead.
6) For a) and b) find x, y, and the measure of each angle.
a) m 1  4x 10 , m 2  10 x  2 y , m 3  6x 12
m1  m2  180o
4 x  10  10 x  2 y  180
m1  m3
4 x  10  6 x  12
10  2 x  12
22  2 x
11  x
4(11)  10  10(11)  2 y  180
44  10  110  2 y  180
164  2 y  180
2 y  16
y 8
1
2
3
m1  4 x  10
m1  4(11)  10
m1  44  10
m1  54
m1  m3
m2  10 x  2 y
m2  10(11)  2(8)
m2  110  16
m2  126
m3  54
7) Let m A  x 2  5 x  39 and m B  4x  31. Find m A and m B if:
a)
A and
B are vertical angles
mA  mB
x 2  5 x  39  4 x  31
x2  9x  8  0
( x  8)( x  1)  0
x  8  0; x  1  0
x  8and1
b)
A and
mB  4 x  31
mB  4(8)  31
mB  32  31
mB  63
mA  63
mB  4 x  31
mB  4(1)  31
mB  4  31
mB  35
mA  35
B form a linear pair
A  B  180
x 2  5 x  39  4 x  31  180
x 2  x  70  180
x 2  x  110  0
( x  11)( x  10)  0
x  11  0; x  10  0
x  11
4
mA  x 2  5 x  39
mA  112  5(11)  39
mA  121  55  39
mA  105
mB  4 x  31
mB  4(11)  31
mB  44  31
mB  75
c)
A and
B are complimentary
mA  mB  90
x 2  5 x  39  4 x  31  90
x 2  x  70  90
x 2  x  20  0
( x  5)( x  4)  0
x5
mA  x 2  5 x  39
mB  4 x  31
mA  52  5(5)  39
mB  4(5)  31
mA  25  25  39
mB  20  31
mA  39
mB  51
mA  (4) 2  5(4)  39
mB  4(4)  31
mA  16  20  39
mB  16  31
mA  75
mB  15
8) Justify each statement:
a) If UV=KL and KL= 6, then UV=6
__Substitution ______
b) If m∠1 + m∠2 = m∠4 + m∠2, then m∠1= m∠4
__Subtraction prop of =_
c) ∠ABC = ∠ABC
__Reflexive Prop =_____
d) If AD bisects BC, then BD ≅ DC.
__bisects→≅seg______
e) If ½m∠D= 45°, then m∠D= 90°.
_Multiplication prop of =
f) If AB = CD, then CD = AB.
__Symmetric Prop =____
9) Write the converse, inverse, and contrapostive of the following conditional
statement. Then decide if each statement is true or false.
Conditional: If a figure is a square, then it is a rectangle.
T
F
Converse:__If a figure is a rectangle, then it is a square______________ T
F
Inverse: __If a figure is not a square then it is not a rectangle_________ T
F
Contrapositive: __If a figure is not a rectangle, then it is not a square____ T
F