CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 6. Polygons and Quadrilaterals

25.

26.

27.Given: ABCDis a rectangleW, X,Y andZare midpoints ofBC, AB, ADandCDrespectivelyProve:

quadrilateralW XY Zis a rhombus

TABLE6.9:

Statements Reasons

7.ABCDis a rectangle 1. Given

8.BW∼=WC, ____, ____, ____ 2. Definition of a midpoint

9.BD=AC 3.

10.XYis a midsegment in 4 ABD

_______,

_______,

_______

4. Definition of a midsegment in a triangle

11.XY=^12 BD=W Zand _______ 5. Midsegment in a triangle is half the length of the

parallel side.

12.^12 BD=^12 AC 6.
13.XY=W Z=Y Z=XW 7.
14.W XY Zis a rhombus 8.
28. Explain why a quadrilateral formed by the segments connecting the midpoints of the sides in a rhombus is
always a rectangle.
29. Explain why a quadrilateral formed by the segments connecting the midpoints of the sides in a square is always
a square.
30. Construct a rhombus with diagonals of lengths 2 inches and 1.5 inches.
31. Construct a rectangle with diagonal length inches.