Question

Given angle 1 is congruent toangle 3 and angle 12 is congruent to angle 8 prove l is parallel to m

Answer 1

Given that;

`\angle1\cong\angle3,\angle12\cong\angle8`

Line a and b are two straight lines cut by two transversal lines l and m.

The tranversal line l shows that;

`\begin{gathered} \angle8\cong\angle6 \\ \end{gathered}`

But also;

`\angle8\cong\angle12`

Thus,

`\angle6\cong\angle12`

Then, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

Thus, line l is parallel to m