a.
To show: Diagonals
a.

Explanation of Solution
Given information:
The coordinates of point C are
The coordinates of point I are
The coordinates of point S are
The coordinates of point O are
Proof:
The coordinates of point Care
The coordinates of point S are
The coordinates of midpoints of
The coordinates of midpoints of
Diagonals
b.
To check:That Diagonals
b.

Answer to Problem 15PSC
Yes,diagonals
Explanation of Solution
Given information:
The coordinates of point C are
The coordinates of point I are
The coordinates of point S are
The coordinates of point O are
Formula used:
Slope of a line:
The coordinates of point C are
The coordinates of point S are
We now check the slopes of isosceles trapezoid CISO.
Slope of
The coordinates of point O are
The coordinates of point I are
Slope of
Since the product of slopes
c.
To Check:That the Diagonals of every isosceles trapezoid are perpendicular.
c.

Answer to Problem 15PSC
No, diagonals are not necessarily perpendicular.
Explanation of Solution
Given information:
The coordinates of point C are
The coordinates of point I are
The coordinates of point S are
The coordinates of point O are
Formula used:
Slope of a line:
The coordinates of point C are
The coordinates of point S are
We now check the slopes of isosceles trapezoid CISO.
Slope of
The coordinates of point O are
The coordinates of point I are
Slope of
Since the product of slopes
If I and S are moved to
The coordinates of point C are
The coordinates of point S are
We now check the slopes of isosceles trapezoid CISO.
Slope of
The coordinates of point O are
The coordinates of point I are
Slope of
Since the product of slopes
d.
To find:The figure to draw to obtain a value of
d.

Answer to Problem 15PSC
The value of
Explanation of Solution
Given information:
The coordinates of point C are
The coordinates of point I are
The coordinates of point S are
The coordinates of point O are
Formula used:
The distance between two points by using the distance formula, which is an application of the Pythagoras theorem.
D
The below theorem is used:
Pythagoras theorem states that “In a right angled
In right
Calculation:
Draw b perpendicular to
The point A lies on x axis. Its y coordinate is 0.The x coordinate will be same as of x coordinate of point O.
The coordinates of point A are
The distance OA can be calculated by applying Pythagoras Theorem.
The distance AS can be calculated by applying Pythagoras Theorem.
In right angle triangle OAS, we get
Chapter 5 Solutions
Geometry For Enjoyment And Challenge
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