Question

explain one way to 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
b use the distance formula to prove that two corresponding sides of the triangles have the same lengths therefore, corresponding angles of the triangles are congruent by cpctc
c use the distance formula to prove that all corresponding sides of the triangles have the same lengths therefore, the two triangles are congruent by sss then, corresponding angles of the triangles are congruent by cpctc
d use the distance formula to prove that two corresponding sides of the triangles have the same lengths therefore, the two triangles are congruent by sas then, all corresponding angles of the triangles are congruent by cpctc

Explanation:

Step1: Recall triangle congruence and CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that if two triangles are congruent, then their corresponding parts (angles and sides) are congruent.

Step2: Analyze each option

• Option A: Opposite - reciprocal slopes imply perpendicular lines, not congruent angles.
• Option B: Two sides being equal is not enough for triangle congruence (needs SSS or SAS etc.).
• Option C: Using the distance formula to prove all corresponding sides are equal (SSS congruence). Then by CPCTC, corresponding angles are congruent.
• Option D: Two sides equal is not sufficient for SAS (need included angle).

Answer:

C. Use the distance formula to prove that all corresponding sides of the triangles have the same lengths. Therefore, the two triangles are congruent by SSS. Then, corresponding angles of the triangles are congruent by CPCTC.