How to prove that two angles are congruent

When you are given some lines and given angles at the intersections, you can pretty much see the answer without using a protractor. Logic is very usefull in these types of situations. If there is a line intersecting between two parallel lines, they will have identical angles on opposite sides of the intersecting line. When a perpendicular line bisects another line, any point on the second line will always be equidistant from any point on the bisecting line. If you have two parallel lines being intersected by another line, and if you rotate the middle of the line by 180 degrees, the angle measurements remain the same. The screenshots below will show you the given tasks on Khan Academy.