-
For numbers 9 15, Supply the missing part of the coordinate proof of the
statement "The segments joining the midpoints of consecutive sides of an isosceles
trapezoid form a rhombus. Choose your answer from the box below.
A.
G.
B. WZ
ſ(-a)²+(-2)
29?+(3
(-b-a
C.
H.
D-a - 0) +(2-0)
V(o--ba)* +(0-3)?
D.
VD2+2ab+a2+c2
E.
2
F. rhombus
Given: Isosceles trapezoid HEAT with HE =TA, W, X, Y AND Z are the midpoints of
the sides.
Prove: Quadrilateral WXYZ is a rhombus
Proof.
Show that WX = XY = YZ = WZ
(9)
WX =
(b-a _ 0)² + ( -c)
E (-b,c) x 0.c)
WX =
(10)
A (5.c)
-b-a
WX =
. (11)
w3)
(2)
2
XY =
ſro - bta)² + (6-8)
XY = 6-2)*+
H(-a,0)
210,0)
T(a,0)
XY =
(12)
ZW=
(14)
yz = C70 - 0) +(-0) )
ZW =
Veza)+(-3)*
YZ =
(13)
ZW =
Vb2+2ab+a2+2
2
Vb2+2ab+a?+c2
YZ =
2
Therefore, WX = XY = YZ = ZW, and WXYZ is_thombus
(15)​