Question

Is △FHK similar to △GHJ ? If so, which postulate or theorem proves these two triangles are similar? ​ △FHK ​ ​ is similar to ​ ​ △GHJ ​ ​ by the ​ ​ SSS Similarity Theorem ​. ​ △FHK ​ ​ is similar to ​ ​ △GHJ ​ ​ by the ​ SSA Similarity Theorem ​. ​ △FHK ​ ​ is similar to ​ ​ △GHJ ​ ​ by the ​ ​ ​ SAS Similarity Theorem. ​ △FHK ​ ​ is not similar to ​ ​ △GHJ ​​. A triangle with vertices F H K. Segment G J is inside the triangle. Point G is on side F H. Point J is on side H K. F G is equal to 12 inches. G H is equal to 10 inches. H J is equal to 15 inches. J K is equal to 18 inches.

Answer 1

△FHK ​ ​ is similar to △GHJ ​ ​ by the ​ ​SAS Similarity Theorem is the answer

Answer 2

Now if we check we can see â H is common between two triangle
now FH/GH=.4545
and HK/HJ=.4545
As FH/GH=HK/HJ
So By SAS Similarity Side-angle-side similarity. When two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, the triangles are similar.
△FHK ​is similar to ​△GHJ ​by the ​SAS Similarity Theorem