Question

If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.

Answer 1

Hence it is proved that all the four angles are right angles.

Steps of construction:

Draw a line AB with a known scale with mid point O.

Draw a line BD perpendicular to line AB with a known scale at point O.

Hence the required construction.

To prove: ∠ AOB = ∠ BOC = ∠ COD = ∠ DOA = 90°

Proof:

∠ AOB = 90°  ..........(1)

(given - one of the four angles formed by two intersecting lines is a right angle)

∠ AOB = ∠ COD   (vertically opposite angles are equal)

∠ COD = 90° ............(2)

Now, consider ∠ AOC

∠ AOC = ∠ AOB + ∠ BOC

180° = 90° + ∠ BOC

∠ BOC = 90° ............(3)

∠ BOC =  ∠ AOD   (vertically opposite angles are equal)

∠ AOD = 90° ............(4)

From (1), (2), (3) and (4) it's clear that, all the angles are right angles.

∴ ∠ AOB = ∠ BOC = ∠ COD = ∠ DOA = 90°

Answer 2

hope the attachment help uh ⬆️

❣️AnSwErEd By AdI❣️