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8.2 Parallelograms
Objectives

Recognize and apply properties of the
sides and angles of parallelograms.

Recognize and apply properties of the
diagonals of parallelograms.
Parallelograms

A quadrilateral with parallel opposite sides is
called a parallelogram ( ABCD).
A
D
B
C
Parallelograms Theorems

Theorem 8.3 – Opposite sides of

Theorem 8.4 – Opposite s in

Theorem 8.5 – Consecutive s in
supplementary.

Theorem 8.6 – If
rt. s.
are ≅.
are ≅.
are
has 1 rt. , then it has 4
Example 1:
Prove that if a parallelogram has two consecutive
sides congruent, it has four sides congruent.
Given:
Prove:
Example 1:
Proof:
Statements
1.
2.
3.
4.
Reasons
1. Given
2. Given
3. Opposite sides of a
parallelogram are .
4. Transitive Property
Your Turn:
Prove that if
Given:
Prove:
and
and
are the diagonals of
,
Your Turn:
Proof:
Statements
Reasons
1.
1. Given
2.
2. Opposite sides of a
parallelogram are congruent.
3.
3. If 2 lines are cut by a transversal,
alternate interior s are .
4.
4. Angle-Side-Angle
Example 2:
RSTU is a parallelogram. Find
and y.
If lines are cut by a transversal,
alt. int.
Definition of congruent angles
Substitution
Example 2:
Angle Addition Theorem
Substitution
Subtract 58 from each
side.
Example 2:
Definition of congruent segments
Substitution
Divide each side by 3.
Answer:
Your Turn:
ABCD is a parallelogram.
Answer:
Diagonals of Parallelograms

Theorem 8.7 – The diagonals of a
bisect each other.

Theorem 8.8 – Each diagonal of a
separates the
into two ≅ ∆s.
Example 3:
MULTIPLE-CHOICE TEST ITEM
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)?
A
B
C
D
Read the Test Item
Since the diagonals of a parallelogram bisect each other,
the intersection point is the midpoint of
Example 3:
Solve the Test Item
Find the midpoint of
Midpoint Formula
The coordinates of the intersection of the diagonals of
parallelogram MNPR are (1, 2).
Answer: C
Your Turn:
MULTIPLE-CHOICE TEST ITEM
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)?
A
Answer: B
B
C
D
Assignment

Pre-AP Geometry:
Pg. 414 #13, 14, 16 – 33, 36, 50

Geometry:
Pg. 414 #4 – 12, 16 – 31