The figure below shows a straight line ab intersected by another straight line t: a segment ab is intersected by a transversal labeled t. angles 1 and 3 and 2 and 4 are vertically opposite angles formed by the transversal on the segment. write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3.

given : a line segment ab is cut by transversal t. ∠1 and ∠3 are vertically opposite angles and ∠2 and ∠4 are vertically opposite angles

to prove : ∠1 = ∠3

proof:

as shown in attachment figure,

as ∠1 and ∠4 makes straight line t so their sum should be equal to 180°

∠1 + ∠4 = 180° (makes pair of supplementary )

similarly ∠3 and ∠4 makes straight line ab so their sum should also be equal to 180°

∠3 + ∠4 = 180° (makes pair of supplementary )

from equations (1) and (2) we get

∠1 + ∠4 = ∠3 + ∠4 (as both were equal to 180°)

subtracting ∠4 from both sides we get

∠1 + ∠4 - ∠4 = ∠3 + ∠4 -∠4

∠1 = ∠3

hence, proved that verticaly opposite angles ∠1 and ∠3 are equal