Question

Given BD bisects ABC and AC is perpendicular to BD prove ABD =CBD by filling out the flow chart

Answer 1

Observe the given figure carefully.

1.

Statement:

`\angle ABD=\angle CBD`

Reason: Angle bisector divides the angles into two equal halves.

2.

Statement:

`BD=BD`

Reason: Side common to both the triangles.

3.

Statement:

`\angle BDA=\angle BDC`

Reason: As AC is perpendicular to BD, the angles BDA and BDC will be 90 degrees.

4.

`\Delta ABD\cong\Delta CBD`

Reason: By using ASA congruence.

Thus, the resulting flow chart can be obtained as follows,