Question

Determine if the triangles, VWZ and VXY, are similar. If so, identify the similarity criterion.

Answer 1

Answer:

The triangles Δ VWZ and Δ VXY are similar by AA criteria.

Step-by-step explanation:

See the attached diagram.

Here, VZ = 16 in and ZY = 8 in. Again, VW = 18 in and WX = 9 in.

Therefore, $\frac{VZ}{ZY} = \frac{VW}{WX} = \frac{2}{1} = 2$

So, line WZ divides the lines VY and VX in the same ratio 2 : 1.

So, Line WZ ║ Line XY

Hence, ∠ XYV = ∠ WZV {The corresponding angles as VY is a transverse}

Again, ∠ YXV = ∠ ZWV {The corresponding angles as VX is a transverse}

Therefore, the triangles Δ VWZ and Δ VXY are similar by Angle-Angle i.e. AA criteria. (Answer)