Question

Which similarity statement expresses the relationship between the two triangles ?

AXYZ-AQRS
AXYZ AROS
AZXY-AQSR
AZXY-AQRS
​

Answer 1

Answer:
`\triangle{ZXY}\sim\triangle{QRS}`

Explanation:

in the given picture , we have two triangles ΔXYZ and ΔRSQ, in which

`\overline{XY}=14=4*3.5=4*\overline{RS}`

`\overline{YZ}=16=4*4=4*\overline{SQ}`

`\overline{ZX}=12=4*3=4*\overline{SR}`

i.e.
`(XY)/(RS)=(YZ)/(SQ)=(ZX)/(QR)=(4)/(1)`

By SSS-similarity postulate, we get

`\triangle{ZXY}\sim\triangle{QRS}`

SSS-similarity postulate says that if the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar