Question

The answer to this.

Answer 1

Answer:

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

Step-by-step 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