Question

Prove: DC = DB

What is the reason for the fourth and eighth steps in the proof?

A.
ASA criterion for congruent triangles
B.
Alternate Interior Angles Theorem
C.
Transitive Property of Equality
D.
Perpendicular Bisector Theorem

Answer 1

d

Explanation:

Answer 2

Option (D)

Explanation:

Statements Reasons

1. DG ⊥ AC 1. Given

2. AG = GC 2. Given

3. DG is the perpendicular bisector of AC 3. deduced from step 1 and 2

4. DA = DC 4. Perpendicular bisector theorem

5. DH ⊥ AB 5. Given

6. AH = HB 6. Given

7. DH is the perpendicular of AB 7. Definition of perpendicular bisector

8. DA = DB 8. Deduced from steps 6 and 7

9. DC = DB 9. Transition property of equality

Therefore, Option (D) will be the answer.