Question

BD is a perpendicular bisector of AC.Which statement can NOT always be proven?

• A. $BD\cong DC$
• B. $AD\cong CD$
• C. $\angle ADB\cong \angle CDB$
• D. $△ABD\cong △CBD$

Answer 1

Answer: (A)

In $△ABD$ and $△BDC$

$AD=CD$ ...... $D$ is the perpendicular bisector of $AC$

$\angle BDA=\angle BDC={90}^{\circ }$

$BD$ is the common side.

Triangles are congruent. SAS Postulate.

Hence the corresponding sides and angles are equal/congruent.

From the options, $BD\cong DC$ is incorrect as they are not the corresponding sides.