Unit 3 HW 9
p. 139 # 7, 9 – 12, 14
7.
Mrs. McCaleb
Statements
NOPRS is equilateral
<OPR = <PRS
OP = SR
PR = RP
ΔOPR = ΔSRP
OR = SP
PT = TR
OT = ST
Reasons
1. Given
Reasons
1. Given
2. Def bisect
3. Given
4.
Statements
YW bisects AX
AW = XW
<A = <X
<5 = <6
<AWY = <XWZ
5.
6.
ΔAWY = ΔXWZ
ZW = YW
1.
2.
3.
4.
5.
6.
7.
9.
1.
2.
3.
2.
3.
4.
5.
6.
7.
Def equilateral
Reflexive
SAS
CPCTC
Given
If = segs are subtracted from = segs,
The differences are =
4. An angle (<ZWY) added to
Congruent angles gives congruent <s
5. ASA
6. CPCTC
10. You have a couple different options on this one; I am going to work it 2 ways:
1) get ΔBCD = ΔEDC, which makes BC = ED, then like multiples are =
2) get ΔACD = ΔADC, which makes AC = CD by CPCTC
1.
2.
3.
4.
5.
6.
7.
8.
9.
Statements
<7 = <8
<7 supp <BCD
<8 supp <EDC
<BCD = <EDC
<ECD = <BDC
CD = DC
ΔBCD = ΔEDC
BC = ED
B is the midpt of AC
E is the midpt of AD
AC = AD
Reasons
1. Given
2. Def linear pair
3.
4.
5.
6.
7.
8.
Supps of = <s are =
Given
Reflexive Property
ASA
CPCTC
Given
9. Like multiples of = segments are =
1.
2.
3.
4.
5.
6.
11.
1.
2.
3.
4.
12.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Statements
<7 = <8
<7 supp <BCD
<8 supp <EDC
<BCD = <EDC
<A = <A
CD = DC
ΔACD = ΔADC
AC = AD
Reasons
1. Given
2. Def linear pair
Statements
PS = PR
<QPS = <QPR
PQ = PQ
ΔRPQ = ΔSPQ
QR = QS
Reasons
1. Given
Statements
HO = MO
JO = OK
<HOJ = <MOK
ΔHOJ = ΔMOK
<HJO = <MKO
HJ is an alt
MK is an alt
<HJK is a right <
<MKJ is a right <
<HJK = 90˚
<MKJ = 90˚
<HJO comp <1
<MKO comp <2
<1 = <2
Reasons
1. Given
3. Supps of = <s are =
4. Reflexive Prop
5. ASA
6. CPCTC
2. Reflexive
3. SAS
4. CPCTC
2.
3.
4.
5.
Vertical angle thm
SAS
CPCTC
Given
6. Def altitude
7. Def right angle
8. Def complementary
9. Complements of = <s are =
OR
4.
5.
HJ = MK
HK = MJ
6.
7.
ΔHJK = ΔMKJ
<1 = <2
4. CPCTC
5. Congruent segs + congruent segs =
congruent segs
6. SSS (or even SAS if you used alt and rt < thms)
7. CPCTC
A
B
C
D
4
1
3
2
Y
14.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
E
Statements
YD = ZD
BD = CD
<BDY = <CDZ
ΔBDY = ΔCDZ
<1 = <4
Draw DE
DE = DE
E is the midpt of YZ
YE = ZE
ΔDYE = ΔDZE
<2 = <3
<BYZ = <CZY
Z
Reasons
1. Given
2. Vertical angle thm
3. SAS
4. CPCTC
5. 2 pts determine a line
6. Reflexive Property
7. Given
8. Def midpt
9. SSS
10. CPCTC
11. Congruent angles plus congruent
Angles makes congruent angles
OR
4.
5.
BY = CZ
BZ = CY
6.
7.
8.
YZ = ZY
ΔBYZ = ΔCZY
<BYZ = <CZY
4. CPCTC
5. Congruent segments plus congruent
Segments makes congruent segments
6. Reflexive
7. SSS
8. CPCTC