Question

In the given figure, if $\angle BAD=\angle CAD$, $\angle ABD=\angle ACD$ , then which of the following is false?

• A. $\Delta ABD\cong \Delta ACD$ by SAS
• B. $\Delta ABD\cong \Delta ACD$ by AAS
• C. $AB=CD$
• D. $BD=CD$

Answer 1

The correct option is C $AB=CD$

In $\Delta ABD$ and $\Delta ACD$
$\angle ABD=\angle ACD\dots \dots \text{(given)}$
$\angle BAD=\angle CAD\dots \dots \text{(given)}$
$AD=AD\dots \dots \text{(common)}$
$\Delta ABD\cong \Delta ACD\text{(AAS postulate)}$
$\therefore AB=AC\dots \dots \text{Corresponding parts of Congruent triangles}$
$\Delta ABD\cong \Delta ACD\text{(SAS postulate)}$
$\Rightarrow BD=CD\dots \dots \text{(Corresponding parts of Congruent triangles)}$