Question 747238
I believe the reason you're looking for on step 3 is the isosceles triangle theorem.  

Since angle BAD is congruent to angle BCD, the sides opposite those angles in triangle ABC are congruent.  

Thus, AB is congruent to CB.  

Assuming this problem looks like a kite, after step 4,

5.  let E be the point of intersection between AC and BD. 

6.  you need to show that triangle ABE is congruent to triangle CBE using ASA (angle side angle).  

7.  Then AE is congruent to CE by CPCTC. (corresponding parts of congruent triangles are congruent.)

8.  Also, angle AEB is congruent to angle CEB by CPCTC 

9.  Angle CEB is congruent to angle AED and angle AEB is congruent to angle CED (vertical angles)

10.  Thus, angle AED is congruent to angle CED (transitive)

11.  ED is congruent to ED (reflexive)

12.  By SAS (side angle side) triangle AED is congruent to triangle CED.

13.  AD is congruent to CD by CPCTC.

14.  Thus, triangle ADC is isosceles by the definition of an isosceles triangle.