To prove that EFGH is a parallelogram, the missing reasons are:
1. Alternate interior angles theorem
2. Reflexive property
3. SAS
4. CPCTC
5. Both pairs of quadrilateral EFGH are congruent, hence, EFGH is a parallelogram.
What is a Parallelogram?
A parallelogram is a quadrilateral that has: two pairs of opposite sides that are parallel and congruent
To prove that EFGH is a parallelogram, we have the following proof which consists of the reasons that jsutifes each given statement:
1. ∠FGE and ∠HEG are alternate interior angles, therefore, ∠FGE ≅ ∠HEG based on the alternate interior angles theorem.
2. EG ≅ EG based on the reflexive property of congruence.
3. ΔFGE and ΔHEG have:
two pairs of corresponding congruent sides - EG ≅ EG, and FG ≅ EH
one pair of included congruent angles - ∠FGE ≅ ∠HEG
Therefore, ΔFGE ≅ ΔHEG by SAS.
4. Since ΔFGE ≅ ΔHEG, therefore, FE ≅ HG by CPCTC.
5. In conclusion, since both pairs of quadrilateral EFGH are congruent, then EFGH is a parallelogram.
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