Geo I
HW 1-19
Name _________________
Date _____________
1. Solve the system:
-2(2x + 3y = 25)
4x – 9y = -55
4x – 9y = -55
4x – 9(7) = -55
4x – 63 = -55
4x = 8
x=2
2. UZ bisects IUQ.
QUZ = 5x + 3y + 1
QUI = 20x + 3y + 3
ZUI = 8x + 2y + 2
20x + 3y +3
-4x – 6y = -50
4x – 9y = -55
-15y = -105
y=7
a)
b)
c)
d)
draw & label a picture
write 2 equations
solve for x & y
find mQUI
Go to the end for the rest of
this problem. (not enough room)
I
Z
5x + 3y +1
U
Q
3. The sum of twice an angle and its complement is 50 less than the angle’s
supplement. Find the measure of the angle’s complement.
2x + 90 – x = 180 – x – 50
x + 90 = -x + 130
2x = 40
x = 20
complement = 70˚
4. Identify all pairs of:
Alt int s 5 & 1, 6 & 4
7
8
5
Alt ext s 8 & 2, 7 & 3
6
4 1
3 2
SSI s 6 & 1, 5 & 4
SSE s 8 & 3, 7 & 2
Corresponding s 6 & 2, 8 & 4, 7 & 1, 5 & 3
Vertical s 6 & 8, 2 & 4, 7 & 5, 1 & 3
Linear pairs 6 & 5,
2 & 1,
6 & 7,
2 & 3,
8 & 5,
4 & 1,
8 & 7,
4&3
A
5. Given: B is the midpoint of AD.
m
n
4
5
8
6
1B
3
2
C
D
7
Give the reason of each statement.
a) m // n
given
b) 1  3
vertical angle thm
d) AB  BD
def midpoint
e) 1  7
// lines  alt int angles
are congruent
h) 4 +5 = 180
g) 2 +3 = 180
def linear pair
// lines  SSE angles sup
c) AB + BD = AD
segment addition
postulate
f) 2 +3 = ABD
angle addition
postulate
**i) m bisects AD
def bisect
6. Every Saturday Mrs. McCaleb sleeps in late.
a) Write the statement as a conditional (if/then)
If it is Saturday, then Mrs. McCaleb will sleep in.
b) Underline p and circle q
c) Write the converse. Is it true or false? If false, why?
If Mrs. McCaleb sleeps in, then it is Saturday. False, I could sleep in on
Columbus Day (which is a Monday).
d) Write the inverse. Is it true or false? If false, why?
If it is not Saturday, then Mrs. McCaleb won’t sleep. False, same as converse
e) Write the contrapositive. Is it true or false? If false, why?
If Mrs. McCaleb does not sleep in, then it is not Saturday.
7. 2x – 5y = 25
-5y = -2x + 25
m = _ 2/5
m // = _2/5
b = -5
m  = -5/2
8. ABC is acute, and QRS is obtuse. Find the restrictions on x and y.
A
B
Q
C
0 < 3x + 15 < 90
-15 < 3x < 75
-5 < x < 25
2. (continued from page 1)
R
90 < 5y – 20 < 180
110 < 5y < 200
22 < x < 40
S
Options for equations:
8x + 2y + 2 = 5x + 3y + 1
3x – y = -1
8x + 2y + 2 + 5x + 3y + 1 = 20x + 3y + 3
13x + 5y + 3 = 20x + 3y + 3
-7x + 2y = 0
2(8x + 2y + 2) = 20x + 3y + 3
16x + 4y + 4 = 20x + 3y + 3
-4x + y = -1
2(5x + 3y + 1) = 20x + 3y + 3
10x + 6y + 2 = 20x + 3y + 3
-10x + 3y = 1
You should have 2 of the 4 equations above. Doesn’t matter which 2!
I am going to use the purple and the green.
Substitution:
-y = -3x – 1
y = 3x + 1
-7x + 2(3x + 1) = 0
-7x + 6x + 2 = 0
-x = -2
x=2
-7(2) + 2y = 0
-14 + 2y = 0
2y = 14
y=7
Elimination (eliminating the y’s)
2(3x – y = -1)
6x – 2y = -2
-7x + 2y = 0
-x
= -2
x=2
-7(2) + 2y = 0
-14 + 2y = 0
2y = 14
y=7
Elimination (eliminating the x’s)
7(3x – y = -1)
3(-7x + 2y = 0)
21x – 7y = -7
-21x + 6y = 0
-y = -7
y=7
-7x + 2(7) = 0
-7x + 14 = 0
-7x = -14
x=2