Question

Which theorem proves ABC=DCB? Why?

Answer 1

Answer:

Parallel postulate : ALTERNATE INTERIOR ANGLES THEOREM.

Step-by-step explanation:

ALTERNATE INTERIOR ANGLES THEOREM : if a transversal cuts 2 parallel lines, then the alternate interior angles are said to be congruent.

( alternate interior angles : in the given figure, DCB and ABC are alternate interior angles.

ACB and CBD are another pair of alternate interior angles.)

[ theorem is an accepted truth or a verified correct statement already i.e, take protractor and measure it will be same in EVERY case. though i have provided the proof below..]

PROOF: since we know that vertically opposite angles will be congruent, so the angle vertically opposite to DCB will be same as DCB. ( refer attachment for vertically opposite angles) now, as corresponding angles will be congruent (see attachment to know what are corresponding angles), the angle vertically opposite to DCB and ABC are corresponding angles. therefore DCB and ABC are also equal

hence,  ABC=DCB.