Parallelogram Proof Requirements

Question 1

Prove a quadrilateral is a parallelogram

Answer 1

• 1 pair of opposite sides is congruent and parallel
• Both pairs of opposite sides are congruent
• Both pairs of opposite sides are parallel
• Both pairs of opposite angles are congruent
• Diagonals bisect each other

Question 2

Prove a quadrilateral is a rectangle

Answer 2

• Diagonals bisect each other and are congruent
• All four angles are right
• Prove it is a parallelogram with at least one right angle
• Prove it is a parallelogram with congruent diagonals

Question 3

Prove a quadrilateral is a rhombus

Answer 3

• Diagonals are perpendicular bisectors of each other
• Both pairs of opposite angles are bisected by the diagonals
• Prove it is a parallelogram with 1 pair of consecutive/adjacent congruent sides
• Prove is a parallelogram with 1 pair of opposite angles bisected by the diagonals
• Prove it is a parallelogram with the diagonals being perpendicular

Question 4

Prove a quadrilateral is a square

Answer 4

• Prove it is a rectangle and rhombus

Question 5

Prove a quadrilateral is a trapezoid

Answer 5

• Only 1 pair of parallel sides and the other sides are not parallel

Question 6

Prove a quadrilateral is a isos. trapezoid

Answer 6

• Prove it is a trapezoid with congruent non-parallel sides
• Prove it is a trapezoid with congruent diagonals
• Prove it is a trapezoid with one pair congruent base angles
• Prove it is a trapezoid with congruent diagonals that are divided proportionally

Question 7

Prove the quadrilateral is a kite

Answer 7

• 2 pairs of disjoint consecutive/adjacent sides are congruent
• Only one diagonal is the perpendicular bisector of the other