Question

opposite sides of a parallelogram are parallel. prove that opposite angles of a parallelogram are congruent. given: abcd is a parallelogram. prove: ∠a ≅ ∠c, ∠b ≅ ∠d. diagram of parallelogram abcd with vertices b, c, a, d labeled statements: 1) $overline{ab} parallel overline{cd}$; 2) $mangle b + mangle c = 180$, $mangle a + mangle d = 180$; 3) $overline{bc} parallel overline{ad}$ reasons: 1) definition of parallelogram; 2) same - side interior angles postulate; 3) dropdown

Explanation:

Step1: Recall parallelogram definition

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. So, since \(ABCD\) is a parallelogram, \( \overline{BC} \parallel \overline{AD} \) by the definition of a parallelogram.

Answer:

Definition of parallelogram