Methods to Proving Quadrilaterals

Question 0

If you think the quadrilateral is a parallelogram…

Answer 0

1. Prove both pairs of opposite sides are congruent
2. Prove both pairs of opposite sides are parallel
3. Prove ONE pair of opposite sides to be congruent AND parallel
4. Prove the diagonals bisect each other
5. Prove both pairs of opposite angles are congruent

Question 1

If you think the quadrilateral is a rectangle…

Answer 1

1. First prove it’s a parallelogram, then either…
   a) Prove it has one right angle
   b) Prove the diagonals are congruent
2. Prove it has FOUR right angles

Question 2

If you think the quadrilateral is a rhombus…

Answer 2

1. First prove it’s a parallelogram, then either…
   a) Prove TWO consecutive sides are congruent
   b) Prove either diagonal bisects the angles to which it is drawn
2. Prove that both diagonals are perpendicular bisectors

Question 3

If you think the quadrilateral is a square…

Answer 3

1. Prove that it is both a rectangle AND a rhombus, which means…
   - it’s a parallelogram
   - it has ONE right angle
   - it has two consecutive sides congruent

Question 4

If you think the quadrilateral is a kite…

Answer 4

1. Prove two disjoint consecutive sides are congruent
2. Prove ONE of the diagonals is the perpendicular bisector of the other
3. Prove ONE of the diagonals bisects a pair of opposite angles

Question 5

If you think the quadrilateral is an isosceles trapezoid…

Answer 5

1. Prove one pair of opposite sides to be parallel, then either…
   a) Prove the non-parallel sides are congruent
   b) Prove the lower OR upper base angles are congruent
   c) Prove the diagonals are congruent