We can use the coordinates of the vertices to calculate the distances between the points.
Using the distances we can show that corresponding sides are congruent.
The Side-Side-Side (SSS) Congruence Postulate then implies that the triangles are congruent.
Method 2 (SAS)
We can cut both triangles in half to get four smaller triangles.
Using the Side-Angle-Side (SAS) Congruence Postulate we can show that these smaller right triangles are congruent.
Since the original triangles are built from two smaller triangles, they are congruent.
Preference
Since the second method does not involve calculation, it can be considered more efficient.
b Let's follow the second method of Part A. Let's cut the triangles with a horizontal and vertical line through point Y, and focus on any two of these smaller triangles.
We can make the following observations about triangles △ ZBY and △ YAX.
They are right triangles, since lines parallel to the coordinate axes are perpendicular. Hence, the angles ∠ A and ∠ B are congruent.
Counting squares, we can see that the legs of these right triangles all have the same length, hence they are congruent.
According to the Side-Angle-Side (SAS) Congruence Postulate, triangles △ ZBY and △ YAX are congruent.
Similar argument shows that all four small triangles are congruent.
If we put together two-two of these congruent triangles, we get two larger triangles of the same shape and size.
Hence, according to the definition of congruence, these larger triangles are congruent.
△ WYZ≅△ WYX
