One of the four angles formed by two intersecting lines is a right angle. Show that the other three angles will also be right angles.

Let AB and CD be the intersecting lines intersecting at O.
Given that one of the angles formed say ∠ AOC = 90° .
∠ AOC and ∠ AOD form a linear pair.
⇒ ∠ AOC +∠ AOD = 180°
    ⇒ 90° + ∠ AOD = 180°
             ∴ ∠ AOD = 180° -90°
                           = 90°
∠ AOC = ∠ DOB (Vertically opposite angles)
∴ ∠ AOC = ∠ DOB = 90°
∠ AOD=∠ BOC (Vertically opposite angles)
∴ ∠ AOD = ∠ BOC = 90°
∴ One of the four angles formed by two intersecting lines is a right angle, then the other three angles will also be right angles.