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kaheart [24]
3 years ago
15

PLS SOMEONE HELP ME QUICKLY

Mathematics
1 answer:
AlekseyPX3 years ago
5 0

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.

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