10. complete the missing reasons in the proof shown below.

Reason 1: Given
With any proof, the first line is always what you are given. You simply repeat it to set up a formal proof. Yes it seems redundant but it's just how proofs are done.

Reason 2: Vertical Angle Theorem
Vertical angles are formed by two lines crossing to form an X shape. The vertical angles are opposite one another. They are congruent angles.

Reason 3: ASA (angle side angle) Congruence Theorem
In statement 1, we found the A and S part, while statement 2 provides the other A allowing us to use ASA. Notice how the segment (S) is between the two angles (A)

Reason 4: CPCTC
Since we know the triangles are congruent (back in statement 3), we know the corresponding pieces are congruent. CPCTC stands for "corresponding parts of congruent triangles are congruent"

Atranslation 6 units to the right and 4 down