State the postulate or theorem that can be used to conclude these triangles are congruent.

SAS
By the vertical angles theorem, what two angles are congruent. 
angle BCA and angle DCE
If AD is an angle bisector of angle A, what two lines can we say are congruent?

BD=DC
What is the reason for statement #1?

Given
State the postulate or theorem that concludes these triangles are congruent.

ASA
By the Alternate Interior Angles Theorem, what two angles are congruent. 
angles 4 and 5
If ED is a perpendicular bisector of line AB, what two sides are congruent. 
AD=DB
What is the reason for statement #3?

Definition of a midpoint
State the postulate or theorem that concludes these triangles are congruent. 
SSS
Assume triangle ABC is congruent to triangle XYZ. What angle is congruent to angle B in triangle XYZ.

angle Y
CD is a perpendicular bisector of AB. If AD=12, what does DB equal?

DB=12
What is the reason for statement #3?

Definition of bisects
State the postulate or theorem that concludes that angle A and angle D are congruent.

Alternate interior angle theorem
What is the value of x.

x=137
If OM is an angle bisector of angle LMN. What is the value of x.

x=7
What is the reason for statement #5?

SSS
State the postulate or theorem that concludes angle ACB and angle DCE are congruent. 
Vertical angles theorem
What is the value of x.

x=5
DB is a perpendicular bisector of AC. Find the value of x.

x=6
What is the reason for #5?

SAS