CB is perpendicular to AD at B between A and D. BCA = BCD and AC = DC. Which congruency statements (HL, AAS, ASA, SAS, and SSS) can you use to conclude that ABC = DBC?

1. are the triangles similar and if so why? what is the value of x? show your work.

Aman is 6 feet 3 inches tall. the top of his shadow touches a fire hydrant that is 13 feet 6 inches away. what is the angle of elevation from the base of the fire hydrant to the top of the man's head?

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.