Question

given that △abc is isosceles with vertex angle b, and bd bisects ∠abc, prove that △adb≅△cdb.
statement reason

1. ab = cb definition of isosceles triangle
2. bd = bd reflexive property of congruence
3. △abc is isosceles with vertex angle b given
4. bd bisects ∠abc given
5. ∠dba = ∠dbc definition of angle bisector
6. △adb≅△cdb sas

the proof shown is written in an incorrect order. what is a possible order that the statements and reasons could be written in?
4, 5, 1, 3, 2, 5
2, 4, 3, 5, 6, 1
none of these
3, 1, 4, 5, 2, 6

Explanation:

Step1: State given info

First, state that $\triangle ABC$ is isosceles with vertex - angle $B$ (3) as it is the given information.

Step2: Use isosceles - triangle def

Then, use the definition of an isosceles triangle to get $AB = CB$ (1).

Step3: State other given

Next, state that $BD$ bisects $\angle ABC$ (4) which is also given.

Step4: Use angle - bisector def

Use the definition of an angle - bisector to get $\angle DBA=\angle DBC$ (5).

Step5: Use reflexive property

Then, use the reflexive property of congruence to get $BD = BD$ (2).

Step6: Prove triangles congruent

Finally, use the Side - Angle - Side (SAS) postulate to prove $\triangle ADB\cong\triangle CDB$ (6).

Answer:

D. 3, 1, 4, 5, 2, 6