Yes, SAS c) d) Yes, SAS or AA e) Yes, SAS f) Yes, AA Given: B K and C L   Prove: ABC HKL To prove two triangles to be similar first find a sequence of similarity transformations that map ABC on to HKL. First dilate by scale factor, k = to get ABC A’B’C’. because dilation is a similarity transformation and using the properties of a dilation: B ABC A’B’C’  B’ and C C’ and B’C’ = k BC = (BC) = KL (B’C’ = KL)  B B’ & B K and C C’ & C L so using the transitive property B’ K and C’ L       and B’C’ = KL due to the dilation. Thus by ASA. A’B’C’  HKL And because was mapped onto using only similarity transformations. ABC HKL ABC HKL AA is a similarity criterion.
c) Yes, SAS d) Yes, SAS or AA e) Yes, SAS f) Yes, AA Given: B  K and C  L Prove: ABC HKL To prove two triangles to be similar first find a sequence of similarity transformations that map ABC on to HKL. First dilate ABC by scale factor, k = to get A’B’C’. ABC A’B’C’ because dilation is a similarity transformation and using the properties of a dilation: B  B’ and C  C’ and B’C’ = k BC = (BC) = KL (B’C’ = KL) B  B’ & B  K and C  C’ & C  L so using the transitive property B’  K and C’  L and B’C’ = KL due to the dilation. Thus A’B’C’  HKL by ASA. And ABC HKL because ABC was mapped onto HKL using only similarity transformations. AA is a similarity criterion.
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