Lessons

1. Basics
 2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Parallelograms

 

Objective:

            •Learning about the basic properties of parallelogram

 

Lesson 5-1 Parallelograms:

            Parallelogram: a quadrilateral with both pairs of opposite sides parallel. 

Theorem 5-1

Opposite sides of a parallelogram are congruent

 

Theorem 5-2

Opposite angles of a parallelogram are congruent.

 

Theorem 5-3

Diagonals of a parallelogram bisect each other. 

 

Theorem 5-4

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

 

Theorem 5-5

If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram

 

Theorem 5-6

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

 

Theorem 5-7

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

 

            Ways  to prove that a quadrilateral is a parallelogram:

          1. Show that both pairs of opposite sides are parallel

         2. Show that both pairs of opposite sides are congruent

         3. Show that one pair of opposite sides are both           congruent and parallel

         4. Show that both pairs of opposite angles and          congruent.

          5. Show that the diagonals bisect each other.

 

 

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