To prove: diagonals of the given parallelogram intersect at their midpoints.
Explanation of Solution
Given:
The parallelogram:
Concept Used:
Midpoint Formula: Midpoint of the line segment joining the two points
To prove that diagonals of the given parallelogram intersect at their midpoints, it is enough to show that both diagonals have same midpoints.
First find the midpoint of the diagonal whose end points are
So applying Midpoint formula on the line segment joining the two points
Now find the midpoint of the diagonal whose end points are
So applying Midpoint formula on the line segment joining the two points
Conclusion:
Both the diagonals have same midpoints, so the diagonals must intersect at their midpoints.
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning