a.
To find: Graph the points
a.
Explanation of Solution
Given information:Points
Graph:
b.
To find:Show that one pair of opposite sides are both congruent and parallel.
b.
Explanation of Solution
Given information:Points
Formula used: The distance between two points
Theslope of a line passing through point
Concept used: In a quadrilateral if one pair of opposite sides are both congruent and parallel then it is a parallelogram.
Calculation:
Here, sides AB and CD are opposite sides.
Since, length of AB and CD are equal.
So, sides AB and CD are congruent.
Since, slopes of
So, sides AB and CD are parallel.
Since, one pair of opposite sides are both congruent and parallel.
Hence,
c.
To find: Show that the diagonals bisects each other (have the same midpoints).
c.
Explanation of Solution
Given information:points
Formula Used:If points are
Calculation:
Here, AC and BD are diagonals of
Let midpoints of
Coordinates of S is
Coordinates of T is
Since both of the midpoints is
So,
Since, both diagonals has same midpoint.
It means that both diagonals intersect each other at
So, diagonals of
If diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Hence,
Chapter 13 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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