Transcript Chapter 8.2 Notes: Use Properties of Parallelograms

Chapter 8.2 Notes: Use
Properties of Parallelograms
Goal: You will find angle and side measures in
parallelograms.
• A parallelogram is a quadrilateral with both pairs
of opposite sides parallel.
• The term “parallelogram PQRS” can be written as
PQRS .
• Theorem 8.3:
If a quadrilateral is a parallelogram, then its opposite
sides are congruent.
If PQRS is a parallelogram, then ______________.
• Theorem 8.4:
If a quadrilateral is a parallelogram, then its opposite
angles are congruent.
If PQRS is a parallelogram, then ______________.
Ex.1: What is true about the two triangles formed by
one diagonal of a parallelogram?
Ex.2: Find the values of x and y.
Ex.3: Find the values of x and y.
• Angles of a polygon that share a common side are
consecutive angles.
• Theorem 8.5:
If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary.
If PQRS is a parallelogram, then ______________.
Ex.4: In ABCD, m1  48o and mBCD  70o. Find
the measures of BAD, 2, 3, 4, 5, 6.
B
5
1
A
C
3
2
6
D
4
• Theorem 8.6:
If a quadrilateral is a parallelogram, then its
diagonals bisect each other.
Ex.5: Given ABCD. Find the value of the variables.
Ex.6: Find the indicated measure in JKLM .
a. NM
b. KM
c. mJML
d. mKML
Ex.7: Given:
LENS
NGTH
Prove: L  T
G
T
E
N
L
S
H