Question

given: parallelogram defg, (overline{dh}congoverline{fi}) prove: (angle dehcongangle fgi) 6. (\triangle dehcong\triangle fgi) 6. side - angle - side 7. click here to insert 7. click here to insert

Explanation:

Step1: Recall the CPCTC theorem

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: Apply CPCTC to the congruent triangles

Since \(\triangle DEH\cong\triangle FGI\) (given in statement 6), by the CPCTC theorem, the corresponding angles \(\angle DEH\) and \(\angle FGI\) are congruent.

Answer:

1. \(\angle DEH\cong\angle FGI\)
2. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)