Question

PLS SOMEONE HELP ME QUICKLY

Answer 1

Given:

In a parallelogram $PRTV, VQ\perp PR,VS\perp RT$.

To prove:

$\dfrac{PQ}{ST}=\dfrac{PV}{VT}$

Solution:

It is given that $VQ\perp PR,VS\perp RT$, it means $\angle PQV$ and $\angle TSV$ are right angle triangles.

In triangle PQV and triangle TSV,

$\angle PQV\cong \angle TSV$         (Right angles)

$\angle QPV\cong \angle STV$         (Opposite angles of a parallelogram)

Two corresponding angles are congruent. So, by AA property of similarity, we get

$\Delta PQV\sim \Delta TSV$

We know that the corresponding parts of similar triangles are proportional. So,

$\dfrac{PQ}{TS}=\dfrac{PV}{TV}$

It can be rewritten as:

$\dfrac{PQ}{ST}=\dfrac{PV}{VT}$

Hence proved.