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1) because they are the two legs of the given isosceles triangle.

2) because the line AB is a perpendicular bisector of line BC.

3) because line AB intersects line DC in a perpendicularly and angle of a perpendicular line to a horizontal line is 90°.

4)because of the perpendicular bisector passing through angle A that divides the angle into 2 equal parts.

5)because it's the same line bisector.

6) because corresponding sides and angles of both triangles are equal.

Step-by-step explanation:

1) AD is approximately equal to AC because they are the two legs of the given isosceles triangle. And the two legs of an isosceles triangle are always equal.

2) AB is perpendicular to BC because of the line AB is a perpendicular bisector of line BC.

3) ∠ABD = ∠ABC are right angles because line AB intersects line DC in a perpendicularly and angle of a perpendicular line to a horizontal line is 90°.

4) ∠ABD = ∠ABC because of the perpendicular bisector passing through angle A that divides the angle into 2 equal parts.

5) AB = AB because it's the same line bisector.

6) Triangle ABC is equal to triangle ABD because corresponding sides and angles of both triangles are equal.

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