Parallelograms
Opposite sides are parallel and equal.
About this topic
A parallelogram has two pairs of parallel sides. Its opposite sides are equal, opposite angles are equal, consecutive angles are supplementary, and the diagonals bisect each other. Proving any of these properties holds is enough to show a quadrilateral is a parallelogram.
Area is base × height, where the height is perpendicular to the base, not the slanted side. Parallelograms model forces in physics, where adding two vectors forms one.
Worked example: in parallelogram ABCD, angle A is 70°. Then angle C is 70°, and angles B and D are each 110°. If the diagonals meet at O and AO = 5, then OC = 5 and AC = 10. To prove a quadrilateral is a parallelogram, show that one pair of opposite sides is both equal and parallel, or that the diagonals bisect each other. With base 8 and height 5, the area is 40, even if the slanted side is 6.
In physics, two forces make the sides of a parallelogram whose diagonal shows the resultant force. A common mistake is using the slanted side as the height, which makes the area too large. The height is the perpendicular distance between the parallel sides. Also remember that consecutive angles add to 180°, not opposite ones, because opposite angles are equal.
Key ideas
- Opposite angles are equal
- Diagonals bisect each other
- Area = base × height
Quick check
Use cases: where Parallelograms helps
- Homework: review the key idea behind Parallelograms before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Parallelograms without notes.
- Visual learning: play with the interactive lab to see how Parallelograms changes when you adjust its inputs.
- Teaching a friend: explain Parallelograms in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Parallelograms?
Opposite sides are parallel and equal.
What will I learn in Parallelograms?
Opposite angles are equal. Diagonals bisect each other. Area = base × height.
Is Parallelograms part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Parallelograms lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Parallelograms?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.