X
R
QTVW is a rectangle.
QW  TV S
Q and T are right s
Q  T A
Given
rect. ⇢ opp sides 
rect. ⇢ right ∡s
All right ∡s

QR  ST
Given
RS  RS
QS  TR S
Reflexive Property
Addition Property (5,6)
SWQ  RVT
SAS (2, 4, 7)
WXYZ is a rectangle.
WZ  XY
S
W and X are right s
W  X A
M is the midpoint of
WX
WM  XM
S
WMZ  XMY
MZ  MY
9. ZMY is isosceles
Given
rect. ⇢ opp sides 
rect. ⇢ right ∡s
All right ∡s

Given
Midpoint ⇢ 2  segs
SAS (2, 4, 6)
CPCTC
9.
 isosceles 
5
6
4
2
31
TBCD is a rhombus
TB  BC  CD  DT S
∡1  2
∡
∡ 3  ∡4
∡5  ∡6
-
A
A
Given
rhombus ⇢ all sides 
rhombus ⇢ opp ∡s 
Given
Subtraction Prop (4, 3)
Vertical ∡s 
RDT  FDC
ASA (5, 2, 6)
RD  DF
CPCTC
1
ABCD is a
AD  CD
∡ 1  ∡2
DP  DP
rhombus
S
A
S
X
2
Given
rhombus ⇢ all sides 
rhombus ⇢ diags. bis. ∡s
Reflexive Property
ADP  CDP
SAS (2, 3, 4)
AP  CP
CPCTC