Question

The answer to this.

Answer 1

The two column proof is presented as follows;

Step
`{}` Statement Reason

1
`{}`
`\overline {AC}` ≅
`\overline {BD}` Given

`{}` ∠CAB ≅ ∠DBA

2
`{}`
`\overline {AB}` ≅
`\overline {AB}` Reflexive property

3
`{}` ΔABC ≅ ΔBAD SAS rule of congruency

Explanation:

Given that we have;

Segment
`\overline {AC}` of ΔABC being congruent to (≅) segment
`\overline {BD}` on ΔBAD and angle ∠CAB on ΔABC is congruent to angle ∠DBA on ΔBAD, and also that the two triangles share a common side, which is segment
`\overline {AB}`, we have;

Segment
`\overline {AB}` is congruent to itself by reflexive property, therefore;

Two sides and an included angle on ΔABC are congruent to the corresponding two sides and an included angle on ΔBAD, which by Side-Angle-Side, SAS, rule of congruency, ΔABC is congruent to ΔBAD