Question

To prove: The similarity of \triangle BCD with respect to \triangle FED. Given information: Here, we have given that \overline{AC}\cong \overline{AE}\ and\ \angle CBD\cong \angle EFD

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asked 2021-04-16
To prove: The similarity of \(\displaystyle\triangle{B}{C}{D}\) with respect to \(\displaystyle\triangle{F}{E}{D}\).
Given information: Here, we have given that \(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{A}{E}}}\ {\quad\text{and}\quad}\ \angle{C}{B}{D}\stackrel{\sim}{=}\angle{E}{F}{D}\)

Expert Answers (1)

2021-04-18
Proof: AS, \(\displaystyle\overline{{{A}{C}}}\stackrel{\sim}{=}\overline{{{A}{E}}}\),
\(\displaystyle\Rightarrow\angle{A}{C}{E}\stackrel{\sim}{=}\angle{A}{E}{C}\) (Angles opposite to equal sides are equal)
Or, \(\displaystyle\angle{B}{C}{D}\stackrel{\sim}{=}\angle{F}{E}{D}\)
Now, In \(\displaystyle\triangle{B}{C}{D}\ {\quad\text{and}\quad}\ \triangle{F}{E}{D}\)
\(\displaystyle\angle{B}{C}{D}\stackrel{\sim}{=}\angle{F}{E}{D}\) (Proved above)
\(\displaystyle\angle{C}{B}{D}\stackrel{\sim}{=}{E}{F}{D}\) (Given)
\(\displaystyle\Rightarrow\triangle{B}{C}{D}\sim\triangle{F}{E}{D}\) (By AA Similarity Rule)
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