What is the similarity theorem is being used?

1. what are the missing reasons in the proof 2. it's in the second picture and 3

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

#1-20 state whether the angles are alternate interior, alternate exterior, vertical, or corresponding angles.