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

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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Ruth Phillips

Step 1

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

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]