Based on the drawing below, in order for \triangle ABC to be similar to \triangle DEF by SAS similarity

Tabansi 2021-08-11 Answered
Based on the drawing below, in order for \(\displaystyle\triangle{A}{B}{C}\) to be similar to \(\displaystyle\triangle{D}{E}{F}\) by SAS similarity, which of the following needs to be true?
image
A.\(\displaystyle{m}\angle{D}={38}^{{\circ}}\)
B.\(\displaystyle{m}\angle{D}={52}^{{\circ}}\)
C.\(\displaystyle{m}\angle{F}={38}^{{\circ}}\)
D.\(\displaystyle{m}\angle{F}={52}^{{\circ}}\)

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Expert Answer

aprovard
Answered 2021-08-12 Author has 10802 answers
Step 1
Angle C needs to be equal to angle F for these triangles to be similar by SSS.
Step 2
For SAS similarity we need two sides and the angle between them.
We see that \(\displaystyle{\frac{{{B}{C}}}{{{A}{C}}}}={\frac{{{E}{F}}}{{{F}{D}}}}={\frac{{{4}}}{{{5}}}}\)
Hence the \(\displaystyle\angle{B}{C}{A}=\angle{E}{F}{D}\Rightarrow\angle{C}=\angle{F}\)
(The angle BC and AC. and the angle between EF and FD)
\(\displaystyle\Rightarrow\angle{F}=\angle{C}={38}^{{\circ}}\)
\(\displaystyle\Rightarrow{m}\angle{F}={38}^{{\circ}}\)
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