Concept explainers
a.
To prove:
a.
Explanation of Solution
Given:
As from the given from figure the
Also from the figure it is given that,
Thus, line l is perpendicular bisector of
Conclusion:
Therefore,
b.
To prove:
b.
Explanation of Solution
Given:
Considering the
Then, according to Side-
So, now it can be said that
Conclusion:
Therefore,
c.
To prove:
c.
Explanation of Solution
Given:
From the given figure,
Considering the line segment
So,
Conclusion:
As the segments AS and SC lie on a single straight line and having a common point, it can be said that
d.
To prove:
d.
Explanation of Solution
Given:
From the part (b), it can be said that
So,
Conclusion:
Therefore, from the above statement it can be concluded that
e.
To prove:
e.
Explanation of Solution
Given:
Considering the triangle
Then, according to Side-Angle-Side theorem of congruency
So, it can be said
Conclusion:
Therefore
f.
To prove:
f.
Explanation of Solution
Given:
Considering the points A and C , there can be only 1 shortest line passing through these points.
Here line segment AC is the shortest straight line passing between these points.
Now point X lies outside the line AC , so if points A and C were connected by a line passing through any point outside the straight line be longer.
In simple words, line segment A-X-C will be longer than line segment A-S-C as the former segment passes through a point outside the shortest straight line between A and C .
Thus,
Conclusion:
As the point X lies outside the shortest straight line between points A and C segment
g.
To prove:
g.
Explanation of Solution
Given:
Calculation:
From the part (b), it was concluded that
And from part (e), it was concluded that
Now, as proven from part (f),
Conclusion:
By using the results from part (b), (e) and (f), it can be easily proved that
Chapter 6 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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