To prove: that if two consecutive sides of a parallelogram are congruent then it is a rhombus.
Explanation of Solution
Given:
A parallelogram with two congruent consecutive sides.
Proof:
Now,
The distance between two parallel lines is equal.
Similarly,
Now,
From equation (i), (ii) and (iii),
Join
Now, the diagonals of a parallelogram bisect each other.
So,
In
Now,
Similarly,
The given quadrilateral is a rhombus.
Hence proved.
Conclusion:
Therefore, the given parallelogram with congruent consecutive sides is a rhombus.
Chapter 5 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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