Question

If a transversal cuts two parallel straight lines and is perpendicular to one of them, show that it will be perpendicular to the other line also.



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Answer 1

Answer:

Let us assume that AB∥CD

Let us assume that AB∥CDPQ is perpendicular to AB

Let us assume that AB∥CDPQ is perpendicular to ABWe have to prove that PQ is perpendicular to CD

Let us assume that AB∥CDPQ is perpendicular to ABWe have to prove that PQ is perpendicular to CD∠PQB=90 degree (given)

Let us assume that AB∥CDPQ is perpendicular to ABWe have to prove that PQ is perpendicular to CD∠PQB=90 degree (given)∴ ∠QRD=∠PQB=90 degree.

∠QRD=∠PQB=90 degree.

∠QRD=∠PQB=90 degree. Corresponding angles of parallel lines

∴ PQ is perpendicular to CD.

Answer 2

Step-by-step explanation:

Let us assume that AB∥CD

PQ is perpendicular to AB

We have to prove that PQ is perpendicular to CD

∠PQB=90 degree

 (given)

∴∠QRD=∠PQB=90 degree

Corresponding angles of parallel lines

∴PQ is perpendicular to CD