acaciablueperso
contestada

In ΔABC shown below, Line segment AB is congruent to Line segment BC:

Given: line segment AB≅line segment BC

Prove: The base angles of an isosceles triangle are congruent.

The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent:


Statement Reason
1. segment BD is an angle bisector of ∠ABC. 1. by Construction
2. ∠ABD ≅ ∠CBD 2. Definition of an Angle Bisector
3. segment BD ≅ segment BD 3. Reflexive Property
4. 4. Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA 5. CPCTC


Which statement can be used to fill in the numbered blank space?

A. ΔDAB ≅ ΔDBC
B. ΔABD ≅ ΔABC
C. ΔABC ≅ ΔCBD
D. ΔABD ≅ ΔCBD

In ΔABC shown below Line segment AB is congruent to Line segment BC Given line segment ABline segment BC Prove The base angles of an isosceles triangle are cong class=

Respuesta :

janak1610

∆ABD≈∆CBD

is the s statement

lublana

Answer:

D.[tex]\triangle ABD\cong \triangle CBD[/tex].

Step-by-step explanation:

Given

In triangle ABC a line segment AB is congruent to line segment BC.

Given: [tex]\overline{ AB} \cong \overline{BC}[/tex]

To prove that the base angles of an isosceles triangle are congruent.

i.e [tex]\angle BAC\cong \angle BCA[/tex]

1.Statement: Segment BD is an angle bisector of [tex]\angle ABC[/tex]

Reason: By construction.

2.Statement: [tex]\angle ABD\cong \angle CBD[/tex]

Reason: By definition of an angle bisector.

3.Statement: [tex]\overline{BD}\cong \overline{BD}[/tex]

Reason: Reflexive property .

4. Statement: [tex]\triangle ABD\cong \traingle CBD[/tex]

Reason: Side-Angle-Side(SAS)

Postulate

5.Statement:[tex]\angle BAC\cong \angle BCA[/tex]

Reason: CPCT.

Hence proved.

Otras preguntas