Question

Fill in the correct reason for A, B, C, D, E, and F to complete the proof above.

Answer 1

(A) Alternate interior angles theorem

(B) Reflexive property

(C) Given

(D) SAS rule of congruency

(E) CPCTC

(F) If both pairs of opposite sides of a parallelogram are congruent, then the quadrilateral is a parallelogram

Explanation:

The two column proof required to prove that EFGH is a parallelogram is presented as follows;

Statement
`{}` Reason

`\overline{FG}`║
`\overline{EH}`
`{}` Given

∠FGE ≅ ∠HEG
`{}` Alternate interior angles theorem

`\overline{EG}` ≅
`\overline{EG}`
`{}` Reflexive property

`\overline{FG}` ≅
`\overline{EH}`
`{}` Given

ΔFEG ≅ ΔHEG
`{}` SAS rule of congruency

`\overline{FE}` ≅
`\overline{HG}`
`{}` CPCTC

EFGH is a parallelogram
`{}` If both pairs of opposite sides of a parallelogram are congruent, then the quadrilateral is a parallelogram

Where CPCTC stands for Congruent Parts of Congruent Triangles are Congruent