Question

Given: See the diagram.

Prove: DC = DB






Statement

Reason

1. given
2. AG = GC given
3. is the perpendicular
bisector of . deduced from steps 1 and 2
4. DA = DC
5. given
6. AH = HB given
7. is the perpendicular
bisector of . definition of perpendicular bisector
8. DA = DB deduced from steps 6 and 7
9. DC = DB Transitive Property of Equality

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

Answer 1

D. Perpendicular Bisector Theorem

Explanation:

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Answer 2

Option D.

Explanation:

Given: See the diagram.

Prove: DC = DB

Perpendicular bisector theorem : If a point lies on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

Proof:

Statement 1:
`\overleftrightarrow{DG}\perp \overline{AC}`

Reason: Given.

Statement 2: AG=GC

Reason: Given

Statement 3:
`\overleftrightarrow{DG}` is perpendicular bisector of
`\overline{AC}`.

Reason: Deduced from steps 1 and 2

Statement 4: DA=DC

Reason: Perpendicular bisector theorem

Statement 5:
`\overleftrightarrow{DH}\perp \overline{AB}`

Reason: Given

Statement 6:AH=HB

Reason:Given

Statement 7:
`\overleftrightarrow{DH}` is perpendicular bisector of
`\overline{AB}`.

Reason: By definition of perpendicular bisector.

Statement 8: DA=DB

Reason : Perpendicular bisector theorem

Statement 9: DC=DB

Reason: Transitive property of equality.

Hence proved.

Therefore, the correct option is D.