Question

The triangles below are similar because of the:

Answer 1

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 $\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}$  , then  △ABC∼△YZX

Here, in ΔABC and  ΔXYZ

AB = 9, BC = x , AC = 12

Similarly, XY = 3, YZ = 2, ZX = 4

Here,

$\frac{AB}{XY} = \frac{9}{3} = 3\\\frac{BC}{YZ} = \frac{x}{2} \\\frac{Ac}{Xz} = \frac{12}{4} = 3$

⇒ 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.