Question

using the figure below, determine if triangle fgh is similar to triangle jki and which similarity postulate applies.
a no, they are not similar.
b yes, they are similar by sas similarity.
c yes, they are similar by aa similarity.
d yes, they are similar by sss similarity.

Explanation:

Step1: Identify corresponding sides

For triangle \(FGH\) and triangle \(JKI\), list the side lengths:

• \(FG = 9\), \(GH = 7.5\), \(FH = 6\)
• \(JK = 6\), \(KI = 5\), \(JI = 4\)

Step2: Check ratios of corresponding sides

Calculate the ratios of the sides:

• \(\frac{FH}{JI}=\frac{6}{4} = 1.5\)
• \(\frac{FG}{JK}=\frac{9}{6}=1.5\)
• \(\frac{GH}{KI}=\frac{7.5}{5} = 1.5\)

Since all three pairs of corresponding sides are in proportion (\(1.5\)), by the SSS (Side - Side - Side) similarity postulate, the triangles are similar.

Step3: Match with options

Option D states "Yes, they are similar by SSS similarity", which matches our conclusion.

Answer:

D. Yes, they are similar by SSS similarity.