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

Tags

CCSS.HSG.C.A.2

Tags

CCSS.HSG.C.A.2

Tags

CCSS.HSG.C.A.2

Tags

CCSS.HSG.C.A.2

• 10
• 5
• 8
• 3

Tags

CCSS.HSG.CO.C.11

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

• supplementary

• congruent

• complementary

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.CO.C.11

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.CO.C.11