1. Section 6.3 Proving Quadrilaterals are parallelograms
Objective:
To determine whether a quadrilateral is a parallelogram
Big idea: reasoning and proof
Essential understanding:
If a quadrilateral’s sides, angles, and diagonals have certain properties, it can be shown that the quadrilateral is a parallelogram.
The properties of parallelograms and algebra can be used to find the lengths of some sides and the measures of some angles of some parallelograms.
Mathematical practice:
Construct viable arguments and critique the reasoning of others

2. Math background
You can decide whether a quadrilateral is a parallelogram if its sides, angles, and diagonals have certain properties. In Section 6.2, you learned theorems about the properties of parallelograms. In this lesson, you will learn the converses of those theorems. So now many properties of parallelograms can be written as biconditional statements

3. Converses of Section 6.2 Theorems
THM 6.8: If both pairs of ____________________ sides of a quadrilateral are ____________________, then the quadrilateral is a parallelogram. THM 6.9: If an ____________________ of a quadrilateral is ____________________ to both of its ____________________ angles, then the quadrilateral is a parallelogram THM 6.10: If both pairs of _____________________ angles of a quadrilateral are _____________________, then the quadrilateral is a parallelogram THM 6.11: If the ____________________ of a quadrilateral ____________________ each other, then the quadrilateral is a parallelogram

4. Proving quadrilaterals are parallelograms
THM 6.12: If ____________________ pair of ____________________ sides of a quadrilateral is both ____________________ and _____________________, then the quadrilateral is a parallelogram

5. Ex: Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain
1. 3.
2. 4.

6. Ex: Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain 5. 6.

7. EX: What value of x and y will make the polygon a parallelogram?
7. 9. 8.

8. EX: show that are the vertices of a parallelogram
Method 1: Definition of Parallelogram Method 2: Opposite sides are congruent

9. EX: show that are the vertices of a parallelogram
Method 3: One pair of opposite sides is congruent and parallel Method 4: Diagonals bisect each other

10. EX: given: prove:
Statements
Reasons