In this example you have two angles marked with double lines telling you they are congruent. Two sides marked congruent with a single dash. Finally, you have a pair of vertical angle which are always congruent. As a result you have two congruent angle and an included side.
In this example you have two triangles that share a common side that is marked congruent. We have two angles at the top marked congruent, and two congruent right angles. Use "ASA" because you have two congruent angles and an included side.
In this example, notice you have two angles marked with double lines. This tells you that the angles are congruent. Next, you have two angles marked with a single line telling you these angles are congruent. Finally, you have a side between these angles with a single mark which tells you these two sides are congruent. So you have two angles and an included side, so use "angle side angle"
The video looks at four sets of triangles and shows you why you can use "ASA" to prove the triangles are congruent.