Quadrilateral Theorems

ABCD is a cyclic quadrilateral with AD = AB and AD is produced to E. If \angle CDE\ =\ 70\degree and \angle CDB\ =\ 72\degree , calculate \angle BAD

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The Opposite Angles Theorem states that opposite angles of a parallelogram are:

• supplementary

• congruent

• complementary

The Opposite Sides Theorem states that a quadrilateral is a parallelogram if:

• both pairs of its opposite sides are parallel.

• both pairs of its opposite sides are congruent.

• both pairs of its opposite sides are perpendicular.

• one pair of its opposite sides are congruent.

• one pair of its opposite sides are parallel.

The Opposite Angles Theorem states that a quadrilateral is a parallelogram if:

• both pairs of its opposite angles are congruent.

• both pairs of its opposite angles are supplementary.

• one pair of its opposite angles are congruent.

• one pair of its opposite angles are supplementary.

The Consecutive Angles Theorem states that a quadrilateral is a parallelogram if:

• it has one angle that is supplementary to each of its consecutive angles.

• it has one angle that is congruent to each of its consecutive angles.

• it has two pairs of consecutive angles that are supplementary.

• it has two pairs of consecutive angles that are congruent.

The Diagonals Theorem states that a quadrilateral is a parallelogram if:

• its diagonals are congruent.

• its diagonals bisect each other.

• its diagonals are perpendicular.

• its diagonals are parallel.