1. Section 6.2 Properties of Parallelograms
OBJECTIVES:
To use relationships among sides and angles of parallelograms.
To use relationships among diagonals of parallelograms.
BIG IDEA: Reasoning and Proof
ESSENTIAL UNDERSTANDINGS:
Parallelograms have special properties regarding their sides, angles, and diagonals.
Parallelograms can be used to prove theorems about parallel lines and their transversals.
MATHEMATICAL PRACTICE:
Construct viable arguments and critique the reasoning of others

2. Math Background
The study of polygons is a study of hierarchy. Quadrilaterals are a subset of polygons and parallelograms are a subset of quadrilaterals. Thus parallelograms have all properties of polygons and quadrilaterals as well as special properties of their own.
Parallelogram: a _________________________ with both pairs of ____________________ sides ____________________
Opposite sides do not share a vertex
Opposite angles do not share a side
Consecutive angles share a side

3. Theorems about Parallelograms
THM 6.3: If a quadrilateral is a parallelogram, then its ____________________ sides are ____________________
THM 6.4: If a quadrilateral is a parallelogram, then its ____________________ angles are ____________________
THM 6.5: If a quadrilateral is a parallelogram, then its ____________________ angles are ____________________
THM 6.6: If a quadrilateral is a parallelogram, then its ____________________ bisect each other

4. Theorem
THM 6.7: If three (or more) ____________________ lines cut off ____________________ segments on one _____________________, then they cut off ____________________ segments on every transversal
EX: What are in the figure?
C D 8
B E
A F

5. EX: Find the measure in the parallelogram HIJK. Explain your reasoning.
1. HI 7. KH H K
2. GH 8. HJ G I J 5. 6.

6. EX: Find the value of each variable in the parallelogram9.
10.

7. EX: Find the value of each variable in the parallelogram
11.
12.

8. EX: Given: Prove:
Statements
Reasons