MCQ
In Fig , if $A B=A C$ and $B D=C D$, then $\angle A B D: \angle A C D=$
- A$1: 1$
- B$1: 2$
- C$2: 1$
- D$2: 3$
✓
Answer
A. $1: 1$
In triangles $A B C$ and $D B C$, we have
$
\begin{array}{ll}
& A B=A C \text { and } D B=D C \\
\Rightarrow & \angle C=\angle B \text { and } \angle D C B=\angle D B C \\
\Rightarrow & \angle C-\angle D C B=\angle B-\angle D B C \\
\Rightarrow & \angle A B D=\angle A C D \Rightarrow \angle A B D: \angle A C D=1: 1
\end{array}
$
In triangles $A B C$ and $D B C$, we have
$
\begin{array}{ll}
& A B=A C \text { and } D B=D C \\
\Rightarrow & \angle C=\angle B \text { and } \angle D C B=\angle D B C \\
\Rightarrow & \angle C-\angle D C B=\angle B-\angle D B C \\
\Rightarrow & \angle A B D=\angle A C D \Rightarrow \angle A B D: \angle A C D=1: 1
\end{array}
$
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