Q:

Which theorem or postulate proves that △ABC and △DEF are similar?Select from the drop-down menu to correctly complete the statement.The two triangles are similar by the ________. A. AA Similarity Postulate B. SSS Similarity Theorem C. SAS Similarity Theorem

Accepted Solution

A:
Answer:△ABC and △DEF are similar by SAS Similarity Theorem.Option (C) is correct .Step-by-step explanation:Definition of SAS Similarity property Two triangles are said to be similar by SAS Similarity property If two sides are proportional and one corresponding angle congruent .In △ABC and △DEF[tex]\frac{ED}{AB}= \frac{7}{21}[/tex][tex]\frac{ED}{AB}= \frac{1}{3}[/tex]and [tex]\frac{EF}{BC}= \frac{11}{33}[/tex][tex]\frac{EF}{BC}= \frac{1}{3}[/tex]Thus[tex]\frac{ED}{AB}=\frac{EF}{BC}= \frac{1}{3}[/tex]∠ABC = ∠DEF  (As given in the figure )Thus △ABC and △DEF are similar by SAS Similarity property .