1. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram.

2. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D

3. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D So segments AD and BC are parallel.

4. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D So segments AD and BC are parallel. And segments AB and DC are parallel.

5. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. There are three SPECIAL parallelograms : Rhombus – all sides are equal with no right angles and opposite angles are equal

6. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. There are three SPECIAL parallelograms : Rhombus – all sides are equal with no right angles and opposite angles are equal Rectangle – opposite sides are equal and all right angles

7. Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram. A Parallelogram is a four – sided figure where opposite sides are parallel. There are three SPECIAL parallelograms : Rhombus – all sides are equal with no right angles and opposite angles are equal Rectangle – opposite sides are equal and all right angles Square – all sides equal and all right angles

8. Polygons – Parallelograms A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles.

9. Polygons – Parallelograms A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent

10. Polygons – Parallelograms A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent

11. Polygons – Parallelograms A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary.

12. Polygons – Parallelograms A Parallelogram is a four – sided figure where opposite sides are parallel. A C B D Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. E

13. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems.

14. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing side…. A B D C 5 5 8 x

15. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing side…. A B D C 5 5 8 x Using # 2, x = 8

16. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing angle…. A B D C x 55

17. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing angle…. A B D C 55 x Using # 4 … x = 125°

18. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing segment BE if segment BD = 20. A B D C E

19. Polygons – Parallelograms Theorems for parallelograms : 1. A diagonal divides a parallelogram into two congruent triangles. 2. Opposite sides are always congruent 3. Any two opposite angles are congruent 4. Any two consecutive angles are supplementary. 5. Diagonals bisect each other. Let’s look at some problems that use these theorems. EXAMPLE # 1 : Find the missing segment BE if segment BD = 20. A B D C E Using # 5, segment BE = 10