Question

What is the missing reason in the proof?Given: ∠ABC is a right angle, ∠DBC is a straight angleProve: ∠ABC ≅ ∠ABDdefinition of angle bisectorsegment addition propertydefinition of congruent anglestransitive property

Answer 1

For a better understanding of the solution provided here please find the relevant diagram drawn as per given information in the file attached.

As given, $\angle ABC=90^{\circ}$. Also, it is given that $\angle DBC$ is a straight angle. Therefore, $\angle DBC=180^{\circ}$.

As can be clearly seen from the diagram, if $\angle DBC=180^{\circ}$ and $\angle ABC=90^{\circ}$, then:

$\angle ABD=\angle DBC-\angle ABC=180^{\circ}-90^{\circ}=90^{\circ}$

Therefore, $\angle ABD\cong\angle ABC$

Hence Proved.