# 5.2 – Parallelograms

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.

Notes

• In the parallelogram, ABCD (in the green box below), $AB \cong DC$ and $BC \cong AD$
• Also, AB || DC and BC || AD.

•  In the above parallelogram, WXYZ, $WX \cong ZY$ and $XY \cong WZ$

• Proofs with Parallelograms (template below)

• Template for Proofs

• Example: Find the length of $\overline{AD}$

• 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 = 3x + 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