Question

draw a line segment AB =5cm .at A, draw AD∆AB ,such that DC = 5cm and parallel to AB . now join CB . measure ∆ABC,∆BCD and length of BC . is figure ABCD a rectangle.​

Answer 1

Here the length of AB = 5cm

DA is perpendicular to AB.

EB is perpendicular to AB.

Two lines perpendicular to the same line are always parallel to each other.

Also ∠1 =∠ 3 = 90°

So ∠1 + ∠3 = 180°

If the sum of co interior angles = 180°, the lines are parallel.

Hence AD || BE

Now we construct the perpendicular bisector of AB which intersects AB at C

Again

∠1= ∠2 = 90°

So

∠1 + ∠2 = 180°

We know If the sum of co interior angles = 180°, the lines are parallel.

Hence AD || CF

Now BE ||AD || CF

Hence all the three lines are parallel to each other.