Solution:
The question asked to prove that
[tex]\angle1\cong\angle3[/tex]
The given statement is
Line l and line m intersect
Linear pair theorem:
In math, the linear pair postulate or linear pair theorem, says the same in mathematical terms. If two angles form a linear pair, then the measures of the angles add up to 180
Also,
Two angles are called supplementary when their measures add up to 180 degrees.
That is,
[tex]\begin{gathered} \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle3\text{ is supplementary to }\angle4 \\ \angle3+\angle4=180^0 \\ \angle1\text{ is supplementary to }\angle4 \\ \angle1+\angle4=180^0 \\ \angle2\text{ is supplementary to }\angle3 \\ \angle2+\angle3=180^0 \\ \angle1\text{ is supplementary to }\angle2 \\ \angle1+\angle2=180^0 \end{gathered}[/tex]
Hence,
Linear pair theorem :
∠1 is supplementary to ∠2
∠2 is supplementary to ∠3
Congruent Supplements Theorem:
If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.
Since angles 1 and 3 are supplements of the same angle 2
Therefore,
With the statement above we can conclude that
∠1 ≅ ∠3 (congruent supplements theorem)
