Prove parallelogram properties NY.Math: GEO‑G.CO.11 Google Classroom Microsoft Teams Share to Microsoft Teams Problem Complete the proof that the diagonals of parallelogram [ABCD] bisect each other. Parallelogram A B C D. Angle D is a right angle. Side A B is parallel to side D C. Side A D is parallel to side B C. There is one line from point A to point C and another line from point B to point D. These lines intersect at a point E. Angle B A E is labeled one. Angle A B E is labeled two. Angle D C E is labeled three. Angle C D E is labeled four. [A] [B] [C] [D] [E] [1] [2] [3] [4] This proof uses the following theorem: Opposite sides of a parallelogram are congruent. Statement Reason 1

[\overline{AB}\parallel\overline{CD}] and

[\overline{AD}\parallel\overline{BC}] Given 2 [\angle 1\cong \angle 3] When a transversal crosses parallel lines, alternate interior angles are congruent. (1) 3 [\angle 2\cong \angle 4] When a transversal crosses parallel lines, alternate interior angles are congruent. (1) 4

[\overline{AB}\cong \overline{CD}] Opposite sides of a parallelogram are congruent. (1) 5

congruence 6

Corresponding parts of congruent triangles are congruent. (5) 7 Point [E] bisects both

[\overline{AC}] and

[\overline{BD}] Definition of bisector (6) Related content