Question

bd bisects \\( \angle abc \\)
reason:
given
\\( \angle a b d \cong \angle c b d \\)
reason:
an angle bisector divides
an angle into two
congruent angles
\\( \angle a d b \cong \angle c d b \\)
reason:
all right angles are
congruent
\\( \overline{b d} \cong \overline{b d} \\)
reason:
reflexive property
\\( \triangle a b d \cong \triangle c b d \\)
reason:
asa
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answer attempt 11 out of 1e+33
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Explanation:

Step1: Recall the ASA (Angle - Side - Angle) congruence criterion

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify the components in \(\triangle ABD\) and \(\triangle CBD\)

• We have \(\angle ABD\cong\angle CBD\) (given by the angle - bisector property).
• \(BD\cong BD\) (reflexive property of congruence, which is the included side).
• \(\angle ADB\cong\angle CDB\) (all right angles are congruent).

Since we have two angles (\(\angle ABD\) and \(\angle ADB\) in \(\triangle ABD\), \(\angle CBD\) and \(\angle CDB\) in \(\triangle CBD\)) and the included side (\(BD\)) congruent, the ASA congruence criterion applies.

Answer:

ASA