contestada

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?

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 g class=
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 g class=
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 g class=

Respuesta :

lublana

Answer:

A. ASA criterion for congruent triangles.

Step-by-step explanation:

Given DG is perpendicular bisector of CA and DH is perpendicular bisector of AB.

In triangle DGC and DGA

DG=DG( reflexive property of equality)

[tex]\angle DGA=\angle DGC=90^{\circ}[/tex] ( given )

[tex]\angle ADG=\angle CDG[/tex] ( by definition of perpendicular bisector)

[tex]\therefore \triangle AGD\cong \triangle CGD[/tex] ( ASA postulate)

Similarly, In triangle ADH and triangle BDH

DH=DH ( reflexive property of equality)

[tex]\angle DHA=\angle DHB=90^{\circ}[/tex] (given)

[tex]\angle ADH=\angle BDH[/tex] ( By definition of perpendicular bisector)

[tex]\therefore \triangle ADH\cong \triangle BDH[/tex] ( ASA postulate)

1.Statement: [tex]\overline{DG}\perp \overline{AC}[/tex]

Reason: Given.

2. Statemnet: AG=GC

Reason: Given

3. Statement: [tex]\overline{DG}[/tex] is perpendicular bisector of [tex]\overline{AC}[/tex]

Reason: from step 1 and step 2.

4.Statement: DA=DC

Reason: ASA criterion for congruent triangles.

5 .Statement:[tex]\overline{DH} \perp \overline{AB}[/tex]

Reason: Given

6.  Statement:AH=HB

Reason:Given

7.Statement: [tex]\overline{DH}[/tex] si perpendicular bisector [tex]\overline{AB}[/tex]

Reason: By definition of perpendicular bisector.

8.Statement: DA=DB

Reason : ASA criterion for congruent triangles.

9.Statement: DC=DB

Reason: Transitive property of equality.

Hence proved.

Answer:

Option D.

Step-by-step 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:  [tex]\overleftrightarrow{DG}\perp \overline{AC}[/tex]

Reason: Given.

Statement 2: AG=GC

Reason: Given

Statement 3: [tex]\overleftrightarrow{DG}[/tex] is perpendicular bisector of [tex]\overline{AC}[/tex].

Reason: Deduced from steps 1 and 2

Statement 4: DA=DC

Reason: Perpendicular bisector theorem

Statement 5: [tex]\overleftrightarrow{DH}\perp \overline{AB}[/tex]

Reason: Given

Statement 6:AH=HB

Reason:Given

Statement 7: [tex]\overleftrightarrow{DH}[/tex] is perpendicular bisector of [tex]\overline{AB}[/tex].

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.

Otras preguntas