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wolfgirl2431
07.04.2021 •
Mathematics
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Ответ:
Step-by-step explanation:
Ответ:
Given : MNPQ is a parallelogram whose diagonals are perpendicular.
To prove : MNPQ is a rhombus.
Proof:
In parallelogram MNPQ,
R is the intersection point of the diagonals MP and NQ( shown in below diagram)
Thus, By SAS postulate of congruence,
By CPCTC,
Similarly,
We can prove,![\triangle MRN\cong \triangle PRN](/tpl/images/0255/4726/c8507.png)
By CPCTC,
But, By the definition of parallelogram,
⇒![MN\cong NP\cong PQ\cong MQ](/tpl/images/0255/4726/66df2.png)
All four side of parallelogram MNQP are congruent.
⇒ Parallelogram MNPQ is a rhombus.
Hence, proved.