Final answer:
To prove two triangles congruent using coordinate geometry, one can apply methods such as SSS or SAS. For SAS, calculate the lengths of two sides using the distance formula and then show that the included angles are equal, using either the law of cosines or inverse trigonometric functions.
Step-by-step explanation:
There are several methods to prove that two triangles are congruent, but two of the most common methods are SSS (Side-Side-Side) and SAS (Side-Angle-Side). To apply one of these methods using coordinate geometry, let's focus on the SAS criterion. To prove two triangles congruent using SAS, we need to show that two sides and the included angle are equal in both triangles.
Let's consider two triangles on a coordinate plane and let's say we need to prove they are congruent. We can calculate the lengths of the corresponding sides using the distance formula (d = √((x2-x1)² + (y2-y1)²)). After calculating the lengths of two pairs of sides, we prove the included angles are equal by using the law of cosines or by calculating the slope of the corresponding sides and then using the inverse trigonometric functions to find the angles. If two sides and the included angle of one triangle are equal to the two sides and included angle of another triangle, then by the SAS criterion, the triangles are congr