6.2 Parallelograms
CCSS
Content Standards
G.CO.11 Prove theorems about parallelograms.
G.GPE.4 Use coordinates to prove simple
geometric theorems algebraically.
Mathematical Practices
4 Model with mathematics.
3 Construct viable arguments and critique the
reasoning of others.
Then/Now
You classified polygons with four sides as
quadrilaterals.
• Recognize and apply properties of the sides and
angles of parallelograms.
• Recognize and apply properties of the diagonals
of parallelograms.
Vocabulary
• Parallelogram:
a quadrilateral with both pairs of opposite
sides parallel
Theorem 6.3:
Vocabulary
Parallelogram Property #1
If a quadrilateral is a parallelogram, then
its opposite sides are congruent.
Theorem 6.4:
Vocabulary
Parallelogram Property #2
If a quadrilateral is a parallelogram, then
its opposite angles are congruent.
Theorem 6.5:
Vocabulary
Parallelogram Property #3
If a quadrilateral is a parallelogram, then
its consecutive angles are
supplementary.
Theorem 6.6:
Vocabulary
Parallelogram Property #4
If a parallelogram has one right angle,
then it has four right angles.
Vocabulary
Parallelogram Diagonal
Theorem 6.7:
Property #1
If a quadrilateral is a parallelogram, then
its diagonals bisect each other.
Vocabulary
Parallelogram Diagonal
Theorem 6.8:
Property #2
If a quadrilateral is a parallelogram, then
each diagonal separates the
parallelogram into two congruent
triangles.
Parallelogram
• Mark in all of the sides and angles
Example 1A
A. ABCD is a parallelogram. Find AB.
A. 10
B. 20
C. 30
D. 50
Example 1B
B. ABCD is a parallelogram. Find mC.
A. 36
B. 54
C. 144
D. 154
Example 1C
C. ABCD is a parallelogram. Find mD.
A. 36
B. 54
C. 144
D. 154
Example
1A of Parallelograms
Use Properties
A. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find AD.
Example
1B of Parallelograms
Use Properties
B. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find mC.
Example
1C of Parallelograms
Use Properties
C. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find mD.
Example 2A
Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.
Example 2B
Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.
Example 2C
Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.
Example 2A
A. If ABCD is a parallelogram, find the value of x.
A. 2
B. 3
C. 5
D. 7
Example 2B
B. If ABCD is a parallelogram, find the value of p.
A. 4
B. 8
C. 10
D. 11
Example 2C
C. If ABCD is a parallelogram, find the value of k.
A. 4
B. 5
C. 6
D. 7
Example 3
Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of the
diagonals of parallelogram MNPR, with vertices
M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
Example 3
Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of the diagonals
of parallelogram LMNO, with vertices
L(0, –3), M(–2, 1), N(1, 5), O(3, 1)?