Question

given: ∠abc is a right angle. ∠dbc is a straight angle. prove: ∠abc≅∠abd. statements reasons 1. ∠abc is a right angle 1. given 2. ∠dbc is a straight angle 2. given 3. m∠abc = 90° 3. definition of right angle 4. m∠dbc = 180° 4. definition of straight angle. what is the missing reason in the proof? definition of congruent angles segment addition property transitive property definition of angle bisector

Explanation:

Step1: Analyze the given angles

We know $\angle ABC = 90^{\circ}$ (right - angle) and $\angle DBC=180^{\circ}$ (straight - angle). Since $\angle DBC=\angle ABD+\angle ABC$, then $\angle ABD=\angle DBC - \angle ABC=180^{\circ}-90^{\circ} = 90^{\circ}$.

Step2: Recall congruent - angle definition

Two angles are congruent if they have the same measure. Since $\angle ABC = 90^{\circ}$ and $\angle ABD = 90^{\circ}$, by the definition of congruent angles, $\angle ABC\cong\angle ABD$.

Answer:

definition of congruent angles