Parallelograms · Years 8–10
In Parallelograms (Years 8–10) you practise 4 skills: Angles in a parallelogram · Sides and diagonals of a parallelogram · Is it a parallelogram? · Parallelograms on a coordinate grid. A parallelogram is a quadrilateral whose two pairs of opposite sides are parallel. Its opposite sides are equal, its opposite angles are equal, and two adjacent angles add up to 180°.
The diagonals of a parallelogram bisect each other: where they meet is the midpoint of each. The area of a parallelogram is the base times the height to it. A quadrilateral is a parallelogram if any one of these holds: both pairs of opposite sides are equal; one pair of opposite sides is both equal and parallel; the diagonals bisect each other; both pairs of opposite angles are equal. One pair of equal sides and the other pair parallel is not enough: an isosceles trapezium looks like that too.
Tip: On a coordinate grid, the step from one vertex to the next is the same as the step along the opposite side. That is how you find the fourth vertex.
What you learn
Angles in a parallelogram
For example: In the parallelogram ABCD it is given that ∢D = 145° . Find ∢A .
Answer and solution
The answer: 35 °
The angles are adjacent, so they add up to 180°: ∢A = 180° − 145° = 35°
Sides and diagonals of a parallelogram
For example: In the parallelogram ABCD two adjacent sides are 17 cm and 3 cm. What is its perimeter?
Answer and solution
The answer: 40 cm
Each side appears twice: 2 × (17 + 3) = 40
Is it a parallelogram?
For example: In the quadrilateral ABCD it is given that AB ∥ DC, AD ∥ BC . Is the quadrilateral a parallelogram?
- Yes, it is a parallelogram
- No, it is not a parallelogram
- You cannot tell
Answer and solution
The answer: Yes, it is a parallelogram
A quadrilateral whose two pairs of opposite sides are parallel is a parallelogram: that is the definition.
Parallelograms on a coordinate grid
For example:
The points A(−5, −6), B(−3, −5), C(−5, 0) are three vertices of the parallelogram ABCD . What are the coordinates of D ?Answer and solution
The answer: (−7, −1)
From B to A you go 2 left and 1 down. The same step from C : D(−7, −1)
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).