Two lines are perpendicular to two parallel lines respectively. Show that these two lines are also parallel.

Question

Two lines are perpendicular to two parallel lines respectively- Show that these two lines are also parallel-

Toppr Admin · Accepted Answer

-because- -AB- and -CD- are perpendicular to -I- and -m-160-therefore -angle APQ - 90-o- and -angle CQM - 90-o-angle APQ - -angle CQM - 90-o-160- -160- -160-Corresponding - angles-therefore- Hence -AB - CD-

Two lines are perpendicular to two parallel lines respectively. Show that these two lines are also parallel.

$$\because$$ $$AB$$ and $$CD$$ are perpendicular to $$I$$ and $$m$$ $$\therefore \angle APQ = 90^o$$ and $$\angle CQM = 90^o$$$$\angle APQ = \angle CQM = 90^o$$ (Corresponding - angles)$$\therefore$$ Hence $$AB || CD$$

$$\because$$ $$AB$$ and $$CD$$ are perpendicular to $$I$$ and $$m$$
$$\therefore \angle APQ = 90^o$$ and $$\angle CQM = 90^o$$
$$\angle APQ = \angle CQM = 90^o$$ (Corresponding - angles)
$$\therefore$$ Hence $$AB || CD$$