SAS similarity

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One of the main 3 main theorems for proving the similarity between $2$ triangles. Similarity (specifically for triangles here) means all the angles in these triangles are equal and all sides are proportional to each other. SAS similarity is a similarity theorem stating that if there are two proportional sides and an angle in between it is equal, then they are similar by SAS similarity.

Example Problem: There are two isosceles triangles, $\triangle ABC$ and $\triangle DEF$. $m\angle B = m\angle E$ = 32^\circ$, and$\overline{AB} = 9$,$\overline{DE} = 3$,$\overline{BC} = 2$,$\overline{EF} = 6$. What are the measures of$m\angle BAC, m\angle BCA, m\angle EDF$and$m\angle EFD$(All of these are base angles for their respective triangles)?

Example Solution: Since sides$ (Error compiling LaTeX. Unknown error_msg)\overline{AB}$and$\overline{DE}$with their common ratio being$3$, and$\overline{EF}$and$\overline{BC}$also having a common ratio of$3$, and both of them sharing a common angle$\angle B$and$\angle E$,$\triangle ABC$and$\triangle DEF$are similar by SAS Similarity. Now, if$2$triangles are similar, all their angles are equal, which means that$m\angle BAC = m\angle BCA = m\angle EDF = m\angle EFD$since they are all base angles of similar triangles. If one of the non-base angles is$32^\circ$, it means that$\frac{(180-32)}{2}$, which is equal to$\frac{148}{2}$, which is$74^\circ$. So$m\angle BAC = m\angle BCA = m\angle EDF = m\angle EFD = 74^\circ$.