Download Theorems for parallelograms

Polygons – Parallelograms
A polygon with four sides is called a quadrilateral. A special type of
quadrilateral is called a parallelogram.
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
D
B
C
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
D
So segments AD and BC are parallel.
B
C
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
D
So segments AD and BC are parallel.
And segments AB and DC are parallel.
B
C
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
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
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
Polygons – Parallelograms
A Parallelogram is a four – sided figure where opposite sides are parallel.
A
D
B
C
Theorems for parallelograms :
1. A diagonal divides a parallelogram into two congruent triangles.
ACD  ABC
Polygons – Parallelograms
A Parallelogram is a four – sided figure where opposite sides are parallel.
A
D
B
C
Theorems for parallelograms :
1. A diagonal divides a parallelogram into two congruent triangles.
2. Opposite sides are always congruent
AD  BC
DC  AB
Polygons – Parallelograms
A Parallelogram is a four – sided figure where opposite sides are parallel.
A
B
D
C
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
A  C
Polygons – Parallelograms
A Parallelogram is a four – sided figure where opposite sides are parallel.
A
D
B
C
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.
A  B  180
B  C  180
Polygons – Parallelograms
A Parallelogram is a four – sided figure where opposite sides are parallel.
A
B
E
D
C
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.
AE  CE
DE  EB
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.
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
8
B
5
D
5
x
C
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
8
B
5
D
5
x
C
Using # 2, x = 8
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
x
D
55
C
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
x
55
Using # 4 … x = 125°
180  55  125
D
C
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
E
D
C
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
Using # 5 , segment BE = 10
E
D
C
20
 10
2