1. Uswatun Khasanah Tika Nurlaeli Nurfeti Dwi S Siti Amidah
KELOMPOK 2
Uswatun Khasanah
Tika Nurlaeli
Nurfeti Dwi S
Siti Amidah

2. Kelompok 1 (hal 274 no 24)
Given : ABCD is a parallelogram E, F, G, and H are midpoints of sides as shown Prove : The figure WXYZ is a parallelogram

3. No
Statements
Reason 1
ABCD is a parallelogram
Given 2
E is the midpoint of
F is the midpoint of
G is the midpoint of
H is the midpoint of 3 ,
Definition of parallelogram 4
Restatement 2,3 5 6
Restatement 4,5 7 8
WXYZ is a parallelogram

4. Kelompok 3 (hal 281 no 34)
Prove that WOZD is a parallelogram. A similar proof will show that AXOW, XBYO, and OYCZ are parallelograms. (hint: First show that AXZD and WYCD are parallelograms.)

5. No
Statements
Reason 1 ,
Given 2
AX = ½ AB
DZ = ½ CD
Definition of midpoint 3
Transitive property 4 5
AW = ½ AD
BY = ½ BC 6 7
Definition of midsegment 8
AXZD is a parallelogram
Definition of parallelogram 9
WYCD is a parallelogram 10 11
OZ = ½ XZ
OX = ½ XZ 12
WOZD is a parallelogram

6. Kelompok 4 (hal 275 no 28) Given : EFGH is a parallelogram. ,
Prove : ABCD is a parallelogram

7. No
Statements
Reason 1
EFGH is a parallelogram
Given 2
Definition of a parallelogram 3 4
dan 5
AF = AE + EF
CH = CG + GH
Definition of between for points 6
AF CH
Restatement 2 and 5 7
Congruent supplements theorem 8
∆ ABF ∆ CDH
SAS postulate 9
CPCTC

8. No
Statements
Reason 10
BG = BF + FG
DE = HD + HE
Definition of between for ponts 11
Restatement 2,3,10 12
Congruent supplements theorem 13
∆ AED ∆ CGB
SAS postulate 14
CPCTC 15
ABCD is a parallelogram
Statements 14 and 20 (definition of a parallelogram

9. Kelompok 5 (hal 280 no 28) Given : ABCD is a parallelogram.
E, F, G, and H are midpoints of , , , and
Prove : EFGH is a parallelogram

10. No
Statements
Reason 1
ABCD is a parallelogram
Given 2
E is midpoint of
F is midpoint of
G is midpoint of
H is midpoint of 3 ,
Definition of parallelogram 4
EF = ½ AB,
HG = ½ CD,
FG = ½ CB,
EH = ½ AD,
Definition of midsegment (Midsegment Theorem) 5
Transitive Property 6
EFGH is a parallelogram

11. Kelompok 6 (hal 281 no 33)
Given : ABCD is any quadrilateral W, X, Y, and Z are midpoints of sides of ABCD as shown. Prove : WXYZ is a parallelogram Plan : add auxiliary segments , , , , and . apply Theorem 8-7 to ∆ABD and ∆BCD.

12. No
Statement
Reason 1
Y is the midpoint of
X is the midpoint of
W is the midpoint of
Z is the midpoint of
Given 2
XY = ½ BD,
Midsegment theorem (theorem 8-7) 3
WZ = ½ BD, 4
Transitive property 5
YZ = ½ AC, 6
XW = ½ AC, 7 8
WXYZ is a parallelogram
Definition of a parallelogram

13. Kelompok 7 (hal 279 no 23)
Given : F is the midpoint of D is the midpoint of E is the midpoint of Prove : AEDF is a parallelogram

14. No
Statements
Reason 1
F is the midpoint of
D is the midpoint of
E is the midpoint of
Given 2
Line l is drawn through B and parallel to
, and is extended to form ∆ BPD
Construction 3
Definisi sudut bertolak belakang 4
Definition of midpoint 5
If two lines parallel are cut by a transversal, then alternate interior angles are congruent 6
∆ DBP ∆ CDF
ASA postulate 7
CPCTC 8
Statement 7, definition of midpoint 9
FD = ½ FP
Algebra 10
BP = CF,
Statement 6 and CPCTC 11
CF = FA ,
Definiton of midpoint

15. No
Statement
Reason 12
BP = FA,
Transitive property, statement 2 13
ABPF is a parallelogram
Definition of parallelogram 14 15
Opposite side of a parallelogram are congruent (definition of a parallelogram 16
FD = ½ AB
Substitution in statements 1 and 15 17
Statement 16 18
Definition of a parallelogram 19
AEDF is a parallelogram

16. THANK YOU