Parallelogram — Geometry, what it means and where it is taught
A quadrilateral with both pairs of opposite sides parallel.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Parallel — Same slope, different intercept.
What uses it later
This idea is needed for:
- Rhombus — A parallelogram with four congruent sides.
Practise this idea
11 questions in the course bank use Parallelogram, in Length and Area in 2-D Figures, Quadrilaterals & Polygon Properties, Coordinate Geometry Proofs, Area of Triangles & Quadrilaterals. The first 8 are below; the rest are in those units.
Problem 1
Find the area of a parallelogram with base 12 and height 5.
Worked answer
60
12 × 5 = 60
Problem 2
Is every square a rectangle?
- Yes
- No
- Only if it is also a rhombus
- Only in coordinate geometry
Worked answer
Yes
A square is a parallelogram with four right angles.
That is exactly a rectangle, plus equal sides.
Problem 3
In parallelogram ABCD, m∠ A = 70°. Find m∠ B.
Worked answer
110
180 - 70 = 110°
Opposite angles would be 70°.
Problem 4
In parallelogram ABCD, m∠ A = 70°. Find m∠ C.
Worked answer
70
∠ A and ∠ C are opposite.
m∠ C = 70°
Problem 5
Congruent diagonals that bisect each other mean the shape is a
- rectangle
- rhombus
- trapezoid
- kite
Worked answer
rectangle
Bisecting diagonals make it a parallelogram.
Congruent diagonals upgrade it to a rectangle.
Problem 6
Perpendicular diagonals that bisect each other mean the shape is a
- rhombus
- rectangle
- trapezoid
- square
Worked answer
rhombus
Bisecting makes it a parallelogram.
Perpendicular makes it a rhombus.
Problem 7
In parallelogram ABCD, m∠ A = (3x+10)° and m∠ C = (5x-30)°. Find x.
Worked answer
20
3x + 10 = 5x - 30
40 = 2x
x = 20
Problem 8
A quadrilateral has diagonals that bisect each other, are congruent, and are perpendicular. Name it.
Worked answer
square
Bisecting: parallelogram.
Congruent: rectangle. Perpendicular: rhombus.
Both together: a square.