Question 12: To prove that quadrilateral CDEF is a parallelogram, we need to show that both pairs of opposite sides are parallel.
Given:
1. Angle FCE congruent Angle DEC (corresponding angles of congruent triangles)
2. Angle FCD congruent Angle DEF (corresponding angles of congruent triangles)
To prove:
CDEF is a parallelogram.
Proof: Since Angle FCE congruent Angle DEC, and Angle FCD congruent Angle DEF, by the Alternate Interior Angles Therorem, EF is parallel to CD.
Similarly, since Angle FCD congruent Angle DEF, and Angle FCE congruent Angle DEC, by the Alternate Interior Angles Theorem, CF is parallel to DE.
Therefore, CDEF is a quadrilateral with opposite sides CF and DE, and EF and CD, which are both parallel.
Hence, by definition, CDEF is a parallelogram. (Now, do the other one yourself or ask help from the teacher! You're most welcome :D glad to help) and if it's wrong im sorry.
