Question

$\angle abd\cong\angle cbd$
reason:
an angle bisector divides
an angle into two
congruent angles
$\angle adb\cong\angle cdb$
reason:
all right angles are
congruent
$\overline{bd}\cong\overline{bd}$
reason:
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given
reflexive property
a segment bisector divides a
segment into two congruent
segments
a midpoint divides a
segment into two congruent
segments
$\triangle abd\cong\triangle cbd$
reason:
select reason
answer attempt 1 out of $1e + 33$
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Explanation:

Step1: Determine the reason for $\overline{BD}\cong\overline{BD}$

The reflexive property of congruence states that any geometric figure is congruent to itself. For the segment $\overline{BD}$, it is congruent to itself. So, the reason for $\overline{BD}\cong\overline{BD}$ is the reflexive property.

Step2: Determine the reason for $\triangle ABD\cong\triangle CBD$

We have $\angle ABD\cong\angle CBD$ (by the angle - bisector property), $\angle ADB\cong\angle CDB$ (all right angles are congruent), and $\overline{BD}\cong\overline{BD}$ (reflexive property). By the Angle - Angle - Side (AAS) congruence criterion, if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

• For $\overline{BD}\cong\overline{BD}$, the reason is "Reflexive Property".
• For $\triangle ABD\cong\triangle CBD$, the reason is "AAS (Angle - Angle - Side)".