Plot the given points on the coordinate plane and connect them with the segments.
Graph:
Proof: see solution.
Practice makes perfect
Let's begin with plotting the given points, which are vertices of the triangles, on the coordinate plane.
Next, we will connect appropriate points with segments to create △ XYZ and △ WYV.
Let's notice that these triangles have one congruent corresponding angle, as ∠ Y≅ ∠ Y by the Reflexive Property. Now, let's recall the Corresponding Angles Postulate.
If parallel lines are cut by a transversal,
then the pairs of corresponding angles
are congruent.
Since both ZX and VW are vertical lines, they are parallel to each other. This means that ∠ YZX and ∠ YVW are congruent angles, just as ∠ YXZ and ∠ YWV.
As we can see, these two triangles have congruent corresponding angles. Therefore, by the Angle-Angle Similarity Theorem, △ XYZ and △ WYV are similar.
