Question

3.

Answer 1

Answer:

3. $\overline{PM}\cong \overline{ON}$ Distances between two parallel lines $\overline{MN} \ and\ \overline{PO}$

4. $\overline{AC}$ = $\overline{CE}$: Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of $\overline{AE}$: Reason;  $\overline{AC}$ = $\overline{CE}$: Definition of midpoint

Step-by-step explanation:

3. A parallelogram is defined as a quadrilateral with two opposite sides equal and parallel and having equal opposite interior angles

MNOP is a parallelogram: Reason; Given

$\overline{PM}\left | \right |\overline{ON}$ : Reason; Opposite sides of a parallelogram

∠NOM ≅ ∠OMP: Reason Alternate interior angles

$\overline{MN}\left | \right |\overline{PO}$: Reason; Opposite sides of a parallelogram

∠NMO ≅ ∠MOP: Reason Alternate interior angles

$\overline{PM}\cong \overline{ON}$ Distances between two parallel lines $\overline{MN} \ and\ \overline{PO}$

4. $\overline{AB}\left | \right |\overline{DE}$ : Reason; Given

∠EAB ≅ ∠AED: Reason; Alternate int. ∠s Thm

∠ABC ≅ ∠EDB : Reason; Alternate int. ∠s Thm

C is the midpoint of  $\overline{BD}$: Reason; Given

$\overline{BC}$ = $\overline{CD}$: Reason; Definition of midpoint

Therefore, ΔACB ≅ ΔDCE: Reason Angle Angle Side (AAS) Theorem

$\overline{AC}$ = $\overline{CE}$: Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of $\overline{AE}$: Reason; Definition of midpoint