Question

are these triangles similar?
(image of two triangles: triangle ihg with sides 64, 48, 32; triangle sqr with sides 57, 28, 54. options: yes, no)

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(HIG\) and \(SQR\), assume the correspondence. Calculate \(\frac{64}{57}\approx1.12\), \(\frac{48}{28}\approx1.71\), \(\frac{32}{54}\approx0.59\)

Step2: Check the similarity condition

By the Side - Side - Side (SSS) similarity criterion, for two triangles to be similar, the ratios of their corresponding sides must be equal. Since \(\frac{64}{57}
eq\frac{48}{28}
eq\frac{32}{54}\)

Answer:

no