Geometry / Unit 7: Polygons and Quadrilaterals
7.2 Properties of Parallelograms
Notes
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
- Opposite sides are congruent.
- Opposite angles are congruent.
- Consecutive angles are supplementary.
- The diagonals bisect each other.
- Example: in parallelogram $ABCD$, $m\angle A = 65^\circ$, so $m\angle C = 65^\circ$ and $m\angle B = m\angle D = 115^\circ$.
Practice
In parallelogram $PQRS$, $m\angle P = 3x + 10$ and $m\angle Q = 2x + 20$. Find $m\angle P$.
Consecutive angles are supplementary: $5x + 30 = 180$, so $x = 30$ and $m\angle P = 100^\circ$.
The diagonals of parallelogram $ABCD$ meet at $E$. $AE = 2y + 3$ and $CE = 4y - 5$. Find $AC$.
Diagonals bisect each other: $2y + 3 = 4y - 5$, so $y = 4$, $AE = 11$ and $AC = 22$.
Which is NOT always true of a parallelogram?
Congruent diagonals are true for rectangles, not all parallelograms.
Ready for more? Take the Unit 7 test.