Answer:
ΔABC and ΔXYZ are SIMILAR by SSS property of similarity.
Step-by-step explanation:
SSS Similarity Theorem:
Two triangles are said to be similar if their CORRESPONDING SIDES are proportional.
In ΔABC and ΔXYZ, if [tex]\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}[/tex] , then △ABC∼△YZX
Here, in ΔABC and ΔXYZ
AB = 9, BC = x , AC = 12
Similarly, XY = 3, YZ = 2, ZX = 4
Here,
[tex]\frac{AB}{XY} = \frac{9}{3} = 3\\\frac{BC}{YZ} = \frac{x}{2} \\\frac{Ac}{Xz} = \frac{12}{4} = 3[/tex]
⇒ Corresponding sides are in the ratio of 3, if BC =6 units
Hence, if BC = 6 units, then the ΔABC and ΔXYZ are SIMILAR by SSS property of similarity.
