Question

Apply the SSS Similarity theorem and use trial and error to examine the ratios of the various sides of the triangles. (a) Which of the two triangles are similar? (b) What is the scale factor of the two similar triangles?

Answer 1

The SSS similarity theorem states that if two triangles are simmilar then the ratios between the corresponding sides will follow the same proportion

For example if triangles ABC and DEF are similar then

`(DE)/(AB)=(EF)/(BC)=(FD)/(CA)`

a. You have to compare both triangles to see if this theorem applies.

1) Triangles JKL and RST

`(RS)/(LJ)=(8)/(10)`
`(ST)/(LK)=(12)/(14)=(6)/(7)`
`(RT)/(JK)=(16)/(18)=(8)/(6)`

The proportion between the corresponding sides is different for the three pairs, the SSS similarity theorem does not apply for these triangles.

2) Triangles JKL and TUV

`(JL)/(UT)=(10)/(14)=(5)/(7)`
`(LK)/(UV)=(14)/(21)=(2)/(3)`
`(JK)/(TV)=(18)/(28)=(9)/(14)`

The proportion between the corresponding sides if different, so the theorem does not apply for these triangles.

3) Triangles RST and TUV

`(RS)/(TU)=(8)/(14)=(4)/(7)`
`(ST)/(UV)=(12)/(21)=(4)/(7)`
`(TR)/(VT)=(16)/(28)=(4)/(7)`

The proportion is the same between the three pairs of corresponding sides. This means that the triangles RST and TUV are similar by SSS

b. The scale factor between the two triangles is 4/7