Consider two pairs of supplementary angles:
∠1 and
∠2, and
∠3 and
∠2.
By the definition of supplementary angles, the sum of the angle measures in each of these pairs is
180∘.
m∠1+m∠2=180∘m∠3+m∠2=180∘
The right-hand sides of the are the same. Therefore, by the the left-hand sides must also be equal.
{m∠1+m∠2=180∘m∠3+m∠2=180∘⇓m∠1+m∠2=m∠3+m∠2
Finally, by using the
m∠2 can be subtracted from each side of the obtained equation.
m∠1+m∠2=m∠3+m∠2⇕m∠1=m∠3
The measures of
∠1 and
∠3 are the same, which indicates that these angles are
congruent.
