Answer:
The next statements are are;
Statement [tex]{}[/tex] Reason
Segment [tex]\overline {DC}[/tex] ≅ Segment [tex]\overline {AB}[/tex] [tex]{}[/tex] CPCTC
[tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] and [tex]\overline {DC}[/tex] ≅ [tex]\overline {AB}[/tex], therefore;
ABCD is a parallelogram [tex]{}[/tex] Parallelogram side theorem
Step-by-step explanation:
Statement [tex]{}[/tex] Reason
Segment [tex]\overline {DC}[/tex] ≅ Segment [tex]\overline {AB}[/tex] by Congruent Parts of Congruent Triangles are Congruent (CPCTC)
Given that [tex]\overline {AD}[/tex] ≅ [tex]\overline {BC}[/tex] and we have that [tex]\overline {DC}[/tex] ≅ [tex]\overline {AB}[/tex], we get;
ABCD is a parallelogram [tex]{}[/tex] Parallelogram side theorem
The parallelogram side theorem states that a quadrilateral is a parallelogram if it has two pairs or sets of congruent opposite sides.
