Transcript Proofs Using Coordinate Geometry LESSON 6-7 Additional Examples Examine trapezoid TRAP. Explain why you can assign the same y-coordinate to points R and A. In.

Proofs Using Coordinate Geometry
LESSON 6-7
Additional Examples
Examine trapezoid TRAP. Explain why you can
assign the same y-coordinate to points R and A.
In a trapezoid, only one pair of sides is parallel.
In TRAP, TP || RA . Because TP lies on the
horizontal x-axis, RA also must be horizontal.
The y-coordinates of all points on a horizontal
line are the same, so points R and A have the
same y-coordinates.
Quick Check
HELP
GEOMETRY
Proofs Using Coordinate Geometry
LESSON 6-7
Additional Examples
Use coordinate geometry to prove that the
quadrilateral formed by connecting the midpoints of
rhombus ABCD is a rectangle.
The quadrilateral XYZW formed by connecting the
midpoints of ABCD is shown below.
From Lesson 6-6, you know that XYZW is a parallelogram.
If the diagonals of a parallelogram are congruent, then the parallelogram is
a rectangle by Theorem 6-14.
HELP
GEOMETRY
Proofs Using Coordinate Geometry
LESSON 6-7
Additional Examples
Quick Check
(continued)
To show that XYZW is a rectangle, find the lengths of its diagonals,
and then compare them to show that they are equal.
XZ =
(–a – a)2 + (b – (–b))2 =
( –2a)2 + (2b)2 =
YW =
(–a – a)2 + (– b – b)2 =
( –2a)2 + (–2b)2 =
4a2 + 4b2
4a2 + 4b2
Because the diagonals are congruent, parallelogram XYZW is a rectangle.
HELP
GEOMETRY