Given:
In a parallelogram
.
To prove:
Solution:
It is given that
, it means
and
are right angle triangles.
In triangle PQV and triangle TSV,
(Right angles)
(Opposite angles of a parallelogram)
Two corresponding angles are congruent. So, by AA property of similarity, we get
We know that the corresponding parts of similar triangles are proportional. So,
It can be rewritten as:
Hence proved.