Unit 4 HW 2
p. 178 # 1 -6, 8, 9, 12
Mrs. McCaleb
A
1.
Given: ΔABD is isosceles with base BD
AC is a median
Prove: AC is the perpendicular bisector of BD
B
D
C
F
2.
G
Given: EFGH is a rhombus
Prove: EG perpendicular to FH
H
E
3.
H
P
J
K
N
Given: ray JK bisects HJL
NP perpendicular HJ
NM perpendicular JL
Prove: NP  NM
M
L
A
4.
Given: ΔABD is isosceles w/ base BD
Ray AC bisects BAD
Prove: AC perpendicular BD
B
C
D
E
5.
Given: EH is an altitude of ΔEFG
Prove: 1  2
F
2 1
H
1.
2.
3.
G
Statements
EH is an altitude of ΔEFG
1 is right
2 is right
1  2
Reasons
1. Given
2. Def altitude
3. Right  Thm
6.
Given: ΔABD is isosceles w/ base BD
AC is a median
A
Prove: ∆ABC  ∆ADC
B
C
D
Statements
ΔABD is isosceles w/ base BD
AC is a median
AB  AD
BC  CD
AC  AC
∆ABC  ∆ADC
1.
2.
3.
4.
5.
A
8.
Reasons
1. Given
2.
3.
4.
5.
Def isosceles
Def median
Reflexive property
SSS
Given: AC is a median
AC is an altitude
Prove: ∆ABD is isosceles
2 1
B
C
1.
2.
3.
4.
4.
5.
6.
7.
D
Statements
AC is a median
AC is an altitude
1 is right
2 is right
1  2
BC  CD
AC  AC
∆ABC  ∆ADC
AB  AD (or B  D)
ΔABD is isosceles
Reasons
1. Given
2. Def altitude
3.
4.
4.
5.
6.
7.
Right  Thm
Def median
Reflexive property
SAS
CPCTC
Def isosceles
A
9.
Given: ΔABD is isosceles w/ base BD
Ray AC and AE trisect BD
Prove: AC  AE
B
C
1.
2.
3.
4.
5.
6.
D
E
Statements
ΔABD is isosceles w/ base BD
AB  AD
B  D
Ray AC and AE trisect BD
BC  ED
∆ABC  ∆ADE
AC  AE
Reasons
1. Given
2. Def isosceles
3.
4.
5.
6.
Given
Def trisect
SAS
CPCTC
A
12.
Given: ΔABD is isosceles w/ base BD
Ray BC bisects ABD
Ray DC bisects ADB
C
B
1.
2.
3.
4.
5.
2
1
D
Prove: ∆BCD is isosceles
Statements
ΔABD is isosceles w/ base BD
ABD  ADB
Ray BC bisects ABD
Ray DC bisects ADB
1  2
∆BCD is isosceles
Reasons
1. Given
2. Def isosceles
3. Given
4. Like divisions of  s are 
5. Def isosceles