Question

bd bisects \angle abc
reason:
given
\angle abd \cong \angle cbd
reason:
an angle bisector divides an angle into two congruent angles
\angle adb \cong \angle cdb
reason:
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given
reflexive property
vertical angles are congruent
all right angles are congruent
an angle bisector divides an angle into two congruent angles
parallel lines cut by a transversal form congruent alternate interior angles
parallel lines cut by a transversal form congruent corresponding angles
answer attempt 1 out of 1e+33
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Explanation:

Step1: Analyze the nature of angles ∠ADB and ∠CDB

These two angles are adjacent and form a linear pair. If they are congruent, they must be right angles.

Step2: Recall the property of right - angles

The property “All right angles are congruent” is applicable here. Since ∠ADB and ∠CDB are right angles (if they are congruent and form a linear pair, each is \(90^{\circ}\)), this property justifies their congruence.

Answer:

All right angles are congruent