Quadrilateral Proofs

Question 1

Quadrilateral

Answer 1

Closed shape that has four sides

Question 2

Parallelogram

Answer 2

1. Opposite sides are congruent
2. Opposite sides are parallel
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Corresponding angles add to 180 degrees

*Note: Any of these properties by themselves (except #5) are enough to prove a quadrilateral is a parallelogram. You can also prove a parallelogram by proving one set of opposite sides is both congruent and parallel

Question 3

Rhombus

Answer 3

Has all the properties of a parallelogram PLUS:

1. Corresponding sides are congruent
2. Diagonals are perpendicular to each other
3. Diagonals bisect the angles

Any one of these are sufficient to prove a parallelogram is a rhombus

Question 4

Rectangle

Answer 4

A rectangle has all of the properties of a parallelogram PLUS:

1. All angles are right angles
2. Diagonals are congruent

*Note: you can prove a parallelogram is a rectangle by proving the shape has at least one right angle

Question 5

Square

Answer 5

• A square is a rhombus with one right angle
• A square is a rectangle with congruent corresponding sides

Question 6

Trapezoid

Answer 6

A trapezoid is a quadrilateral with the following properties:

1. One pair of opposite sides is parallel
2. Adjacent angles formed by two different base angles add to 180 degrees

Question 7

Isosceles Trapezoid

Answer 7

An isosceles trapezoid has all of the angles of a trapezoid PLUS:

• The two opposite sides that are not parallel are congruent
• Base angles are congruent
• Diagonals are congruent
• Median from non-parallel sides is parallel to the bases

Question 8

Kite

Answer 8

A kite has the following properties:

1. Two pairs of adjacent sides are congruent
2. Diagonals are perpendicular to each other
3. One diagonal bisects the other
4. One pair of opposite angles are congruent
5. The diagonal bisects the other pair of angles