How to Prove a Quadrilateral is a...

Question 1

A quadrilateral is a parallelogram if

Answer 1

1. both pairs of opposite side sides are congruent
2. If both pairs of opposite sides are parallel
3. One pair of opposite sides is both parallel and congruent
4. If diagonals bisect each other
5. If both pairs of opposite angles of a quadrilateral are congruent

Question 2

How to know if a parallelogram is a rectangle

Answer 2

1. If a //gm contains at least one rt angle
2. If the diagonals of a //gm are congruent
3. If all 4 angles of a quadrilateral are rt angles

Question 3

How to know a quadrilateral is a kite

Answer 3

1. If 2 disjoint pairs of consecutive sides are congruent
2. If one of the diagonals is the perpendicular bisector of the other diagonal

Question 4

How to know if a quadrilateral is a rhombus

Answer 4

1. If //gm has a pair of consecutive congruent sides
2. If a diagonal of a //gm bisects 2 angles
3. If the diagonals of a quadrilateral are perpendicular bisectors of EACH other

Question 5

How to know if a quadrilateral is a square

Answer 5

1. If a quadrilateral is both a rectangle and square.

Question 6

How to know if a quadrilateral is an isosceles trapezoid

Answer 6

1. If a trapezoid’s non-parallel sides are congruent
2. If the lower and upper base angles of a trapezoid are congruent
3. If the diagonals of a trapezoid are congruent