Question

question 1 of 10
determine which postulate or theorem can be used to prove that
$\triangle abd\cong\triangle cbd$.
a. sss
b. sas
c. asa
d. aas

Explanation:

• Identify the given information:
• From the figure, we know that \(AD = CD\) (marked as equal).
• \(\angle ADB=\angle CDB\) (marked as equal).
• \(BD = BD\) (common side in both \(\triangle ABD\) and \(\triangle CBD\)).
• Recall the triangle - congruence postulates:
• The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
• In \(\triangle ABD\) and \(\triangle CBD\), we have two sides (\(AD = CD\) and \(BD=BD\)) and the included angle (\(\angle ADB=\angle CDB\)) equal.

Answer:

B. SAS