Question

d is the midpoint of \\( \overline { a c } \\)
reason:
given
\\( \overline { a d } \cong \overline { c d } \\)
reason:
a midpoint divides a segment
into two congruent segments.
\\( \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:
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sss
sas
asa
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answer attempt 2 out of 2
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Explanation:

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

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

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

• We have \(AD\cong CD\) (side), \(\angle ADB\cong\angle CDB\) (angle), and \(BD\cong BD\) (side). The angle \(\angle ADB\) is included between \(AD\) and \(BD\) in \(\triangle ABD\), and the angle \(\angle CDB\) is included between \(CD\) and \(BD\) in \(\triangle CBD\).

Answer:

SAS