Question

Draw a line segment AB = 6 cm. Mark two points P and Q on it. Draw lines
perpendicular to AB through P and Q (PR and QS). What can you say about PR and
QS? Are these parallel? Justify your answ​

Answer 1

Since PR ⊥ AB & QS ⊥ AB

∠ QPR = ∠ PQS = 90 °

Join R & S such that RS || AB

Mark a point X on extended PR and Y on extended QS

Now PR and QS are transversals on AB & RS

Since corresponding angles of a transversal are equal

∠ QPR = ∠SRX = ∠ PQS = ∠ RSY = 90 °

Now since ∠ PRS + ∠ SRX = ∠ QSR + ∠ RSY = 180 °

∠ PRS = ∠ SRX = ∠ QSR = ∠ RSY = 90 °

Impies PQSR is either a square or a rectangle since all angles are right angles

Now since opposite sides of squares and rectangles are parallel

PR || QS

:-)