What is the reason for statement 5 in this proof?

given: δabc, where ab = bc (view diagram)
prove: m∠bac=m∠bca

statement
reason
1. let δabc be an isosceles triangle with
ab = bc.

given

2. create point d on side ac so bd bisects
∠abc.

constructing an angle bisector

3. m∠abd=m∠cbd

definition of angle bisector

4. bd = bd

reflexive property of equality

5. δabd≅δcbd

6. m∠bac=m∠bca

corresponding angles of congruent triangles have equal measures.

a. asa

b. sss

c. aas

d. sas

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.