# Proving properties of Quadrilaterals Wrksht ```Team Parallelogram:
Definition of a Parallelogram:
A parallelogram is a quadrilateral with opposite sides parallel.
Today you will prove the following properties of parallelograms:
1. The opposite sides are congruent
2. The opposite angles are congruent
3. The diagonals bisect each other
4. Any pair of consecutive angles are supplementary
Once you have proved a property, you may use it in proving subsequent
properties.
Property 1:
Property 2:
Property 3:
Property 4:
Team Rectangle
Definition of a Rectangle
A rectangle is a parallelogram in which at least one angle is right. Thus a
rectangle has four right angles.
Today you will prove the following Properties of Rectangles:
1. All angles of a rectangle are right angles.
2. The diagonals are congruent.
Remember the following are properties of parallelograms:
1. The opposite sides are congruent
2. The opposite angles are congruent
3. The diagonals bisect each other
4. Any pair of consecutive angles are supplementary
Once you have proved a property, you may use it in proving subsequent
properties.
Property 1:
Team Kite
Definition of a Kite
A kite is a quadrilateral with two sets of consecutive sides congruent. (those two
sets cannot share a side, they must be disjoint).
Today you will prove the properties of a kite:
1. The diagonals are perpendicular
2. One diagonal bisects the other.
3. One diagonal bisects a pair of opposite angles
4. One pair of opposite angles is congruent
Once you have proved a property you may use it to prove subsequent
properties.
Property 1
Property 2
Property 3
Property 4
Team Rhombus
Definition of a Rhombus
A rhombus is a parallelogram with at least one set of consecutive sides
congruent.
Today you will prove the following properties of a Rhombus
1. All four sides of a rhombus are congruent
2. The diagonals are perpendicular bisectors of each other
3. The diagonals bisect opposite angles
4. The diagonals create right isosceles triangles
Remember that rhombuses are parallelograms and kites, so the following
properties apply:
Properties of a kite:
1. The diagonals are perpendicular
2. One diagonal bisects the other.
3. One diagonal bisects a pair of opposite angles
4. One pair of opposite angles is congruent
Properties of parallelograms:
1. The opposite sides are congruent
2. The opposite angles are congruent
3. The diagonals bisect each other
4. Any pair of consecutive angles are supplementary
Property 1
Property 2
Property 3
Properties of Isosceles Trapezoid
Definition of an Isosceles trapezoid
An isosceles trapezoid is a quadrilateral with one set of parallel sides, with the
non-parallel sides congruent.
Today you will prove the properties of an Isosceles Trapezoid:
1. The lower base angles are congruent
2. The upper base angles are congruent
3. The diagonals are congruent
4. Any lower base angle and upper base angle are supplementary
Property 1
Property 2
Property 3
Property 4
```