Answer: [tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]
Step-by-step explanation:
in the given picture , we have two triangles ΔXYZ and ΔRSQ, in which
[tex]\overline{XY}=14=4\times3.5=4\times\overline{RS}[/tex]
[tex]\overline{YZ}=16=4\times4=4\times\overline{SQ}[/tex]
[tex]\overline{ZX}=12=4\times3=4\times\overline{SR}[/tex]
i.e. [tex]\dfrac{XY}{RS}=\dfrac{YZ}{SQ}=\dfrac{ZX}{QR}=\dfrac{4}{1}[/tex]
By SSS-similarity postulate, we get
[tex]\triangle{ZXY}\sim\triangle{QRS}[/tex]
SSS-similarity postulate says that if the lengths of the corresponding sides of two triangles are proportional, then the triangles must be similar
