**Key Terms**

- Bisect – To divide into two equal parts.
- Consecutive Angles – Angles that are side-by-side.
- Opposite Angles – Two angles that are not consecutive.
- Opposite Sides – Two sides that are not consecutive.
- Parallel – Lying in the same plane without intersecting.
- The symbol || means “parallel.”
- If parallel lines are graphed on a Cartesian coordinate system, they have the same slope.

- Parallelogram – A quadrilateral in which the opposite sides are parallel and congruent

**Review**

- Parallel Lines
- They are coplanar (in the same plane).
- They never intersect.
- They are always the same distance apart.

- Quadrilateral – Polygon with 4 sides.

- Consecutive interior angles are supplementary (add up to 180°)
- We learned this while studying parallel lines cut by a transversal. Review this concept here:
- http://newvillagegirlsacademy.org/math/?page_id=854

**Notes**

- In the parallelogram, ABCD (in the green box below), and
- Also, AB || DC and BC || AD.

- In the above parallelogram, WXYZ, and

- Proofs with Parallelograms (template below)

- Template for Proofs

- Example: Find the length of

- Remember: AD and BC are congruent, so set them equal to one another.
- 14 + 2x = 6 + 6x
- Subtract 2x on both sides: 14 = 6 + 4x
- Subtract 6 on both sides: 8 = 4x
- Divide by 4 on both sides: 2 = x
- Substitute 2 into x for AD: 14 + 2(2)
- Solve: 14 + 4 = 18

- Example: Find x and y

- Remember: Consecutive interior angles are supplementary (180°), so 110 + 2y must equal 180.
- 110 + 2y = 180
- Subtract 110 on both sides: 2y = 70
- Divide by 2 on both sides: y = 35.
- Since 2y = 70, we can replace 2y with 70 when we solve for x.
- 70 = 5x
- Divide by 5 on both sides: 14 = x.

- Example: Given
*ABCD is a parallelogram*,*AC*= 38, and*AE*= 3*x*+ 4, find the value of*x*.

- Remember: Diagonals of a parallelogram BISECT each other; so, if AE = 3x + 4, then EC must also equal 3x + 4
- Also, if AC is 38, then bisect it (cut it in half); so, AE = 19 and and EC = 19.
- Set up: 3x + 4 = 19
- Subtract 4 on both sides: 3x = 15
- Divide by 3 on both sides: x = 5