Answer:
C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SSS.Then , corresponding angles of the triangles are congruent by CPCTC.
Step-by-step explanation:
We have to explain one way through which we can verify that the corresponding angles of the two triangles are congruent.
A. Use the slope formula to prove that the slopes of corresponding sides are opposite reciprocals . Therefore, the corresponding angles of the triangles are congruent.
In this option we are given that by slopes formula the slopes of corresponding sides are opposite reciprocals .It means sides are perpendicular but not give any information about congruency of two triangles through which we can say corresponding angles of two triangles are congruent.Hence, it is false.
B.Use the distance formula to prove that two corresponding sides of the triangles have same lengths. Therefore, corresponding angles of the triangles are congruent by CPCTC.
In this option we are given information about only two corresponding sides of two triangles . It is not sufficient to prove that corresponding angles of two triangles are congruent.Hence, it is false.
C.Use the distance formula to prove that all corresponding sides of the triangles have same lengths.Therefore,the two triangles are congruent by SSS. Then, corresponding angles of the triangles are congruent by CPCTC.
In this option we have complete information through which we can verify that corresponding angles of two triangles are congruent.Hence, it is correct.
D.Use the distance formula to prove that two corresponding sides of the triangles have same lengths.Therefore, the two triangles are congruent by SAS.Then, all corresponding angles of the triangles are congruent.
In this option we have no complete information through which we can two triangles are congruent by SAS. Therefore, In this option explaination are not given properly.Hence , it is false.
