Determine whether the two triangles are similar. Explain 1. The two tr

skeexerxo175o 2021-11-21 Answered
Determine whether the two triangles are similar.
Explain
1. The two triangles are not similar. Since \(\displaystyle{m}\angle{B}\ne{m}\angle{F}\), the triangles are not similar by the AA criterion.
2. The two triangles are similar. By the Interior angles theorom, \(\displaystyle{m}\angle{C}={67}^{{\circ}}\), so the triangles are similar by the AA criterion.
3. The two triangles are similar. By the interior angles theorem, \(\displaystyle{m}\angle{c}={57}^{{\circ}}\), so the triangles are similar by the AA similarity criterion.
3. The two triangles are not similar. By the interior angles theorem, \(\displaystyle{m}\angle{C}={57}^{{\circ}}\) so, the triangles are not similar by the AA similarity criterion.
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Expert Answer

Ruth Phillips
Answered 2021-11-22 Author has 1100 answers

Step 1
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In \(\displaystyle\triangle{A}{B}{C}\)
\(\displaystyle\angle{B}+\angle{A}+\angle{C}={180}^{{\circ}}\)
\(\displaystyle{48}^{{\circ}}+{65}^{{\circ}}+\angle{C}={180}^{{\circ}}\)
\(\displaystyle\angle{C}={180}^{{\circ}}-{\left({48}+{65}^{{\circ}}\right)}\)
\(\displaystyle\angle{C}={67}^{{\circ}}\)
Step 2
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In \(\displaystyle\triangle{D}{E}{F}\)
\(\displaystyle\angle{D}+\angle{E}+\angle{F}={180}^{{\circ}}\)
\(\displaystyle{65}^{{\circ}}+\angle{E}+{67}^{{\circ}}={180}^{{\circ}}\)
\(\displaystyle\angle{E}={180}^{{\circ}}-{\left({67}^{{\circ}}+{65}^{{\circ}}\right)}\)
\(\displaystyle\angle{E}={48}^{{\circ}}\)
Now in \(\displaystyle\triangle{D}{E}{F}\) and \(\displaystyle\triangle{A}{B}{C}\)
\(\displaystyle\angle{D}=\angle{A}={65}^{{\circ}}\)
\(\displaystyle\angle{E}=\angle{B}={48}^{{\circ}}\)
\(\displaystyle\Rightarrow\triangle{D}{E}{F}\sim\triangle{A}{B}{C}\) [By AA criteria]

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