Question

$\overline{AD}$ is perpendicular to $\overline{BD}$, $\overline{AC}$ is perpendicular to $\overline{BC}$, and $\overline{AD}\cong \overline{BC}$ as shown in the figure above. Determine which of the following congruences is NOT necessarily true.

• A. $\overline{AC}\cong \overline{BD}$
• B. $\overline{AD}\cong \overline{AE}$
• C. $\overline{AE}\cong \overline{BE}$
• D. $\angle DAB\cong \angle CBA$
• E. $\angle EAB\cong \angle EBA$

Answer 1

Answer: (B)

In $△ABC$ and $△ABD$

$AD\cong BC$

$\angle ADB=\angle BCA={90}^{\circ }$

$AB$ is common side

Hence, the triangles are congruent. SAS postulate.

If 2 triangles are congruent, then the corresponding sides and angles are also equal.

In the given options, $AD\cong AE$ is not necessarily true as they are not the corresponding sides.