Parallelograms are a kind of quadrilateral (a 4-sided shape with two identical sides) with opposite angles that don’t have the same measure. Parallelograms come in different flavors, but all of them share the same uniqueness. If you look at any parallelogram, you can see that it has two sets of parallel sides. These parallel sets of sides are known as “adjacent” and “non-adjacent” sides. Each side is either adjacent or non-adjacent to another side on the other end. In this article, we will be discussing whether or not parallelograms have right angles and why? Read on to know more.
Do Parallelograms Have Right Angles?
In geometry, the term “parallel” means that two or more lines are in the same plane. A line can be parallel to a straight line, a curve, or another line. Two lines may be in the same plane regardless of their length but only if they are coplanar. If two lines do not intersect or touch each other, then they are said to be parallel.
What Is A Parallelogram?
A parallelogram is a quadrilateral with two sides that are parallel to each other. A parallelogram is a 2D shape. It has no height. A parallelogram has four sides. Just like a rectangle, a parallelogram also has two pairs of parallel sides. A parallelogram is also a rectangle, but with one side longer than the other. A parallelogram can also be a rhombus, but with both pairs of sides having the same length. A parallelogram can also be a square, but with both pairs of sides having the same length. A parallelogram can also be a kite, but with both pairs of sides having the same length. Parallelograms have many uses in geometry. You can use them to solve many geometry problems.
Why Don’t Parallelograms Have Right Angles?
Two Lines are Parallel
Parallelograms can have more than one pair of parallel sides. The diagram below shows a parallelogram with two pairs of parallel sides. The lines AB and CD are both parallel to line AB. Lines BC and CD are also both parallel to the line AC. Since two lines are parallel, they will always have the same angle between them. For example, in the diagram below, if you were to draw a line from point A to point B and another line from point C to point D, then the angles between these lines will always be equal (all angles will be equal).
Two Lines Have an Angle
The angles between two lines are always different when they intersect at some point (see diagram above). If you were to draw a line from point A to point B and another line from point C to point D, then this intersection would not be in a straight line (see diagram below). This means that there is no the same angle.
Two Lines are Coplanar
Parallelograms can also have two pairs of parallel sides that are not coplanar. The lines AB and AC do not intersect or touch each other, but they are still parallel. The diagram below shows a parallelogram with two pairs of non-coplanar parallel sides.
Parallelograms Have No Height
Parallelograms can have no height, like the following diagram the same angle between them. Line AB will always have the same angle as line AC.
Two Lines are Parallel, but they are not Coplanar
Parallelograms can also have more than one pair of parallel sides, but they may not be coplanar. The above diagram shows a parallelogram with two pairs of parallel sides that are not coplanar. The lines AB and AC are both parallel to line BC, but they do not intersect or touch each other. Since two lines are parallel, these lines will always have the same angle between them; however, these lines cannot be coplanar since they do not touch each other or intersect.
Two Lines have different lengths and different angles
Parallelograms can also have more than one pair of parallel sides that differ in length and/or angle from each other. In this case, the lines may intersect at some point(s). In this case, both e the same angle between them.
Two Lines are Coplanar
Parallelograms can have two pairs of parallel sides that intersect or touch each other (a point is considered to be a pair of parallel sides if it touches another pair). Consider the parallelogram below. The lines AB and AC are coplanar, but they do not intersect or touch each other. Since two lines are coplanar, they will always have the same angle between them.
One Line is Parallel to Another Line
Parallelograms can also have one side that is parallel to another line (a line is considered to be a pair of parallel sides if it touches another line). The diagram below shows a parallelogram with one side parallel to line AB. Since one line is parallel to another, it will always have the same angle between them.
When Do Parallelograms Have Right Angles?
- If a right angle is formed by two lines that are parallel to each other.
- If the angles of the parallelograms formed by two lines are equal.
- If the angles of the parallelograms formed by two lines are not equal but opposite (180 degrees).
- If a line is parallel to another line and both of them are in the same plane, then they will have right angles, because they intersect at a single point.
- If a line is parallel to another line and one of them is in the same plane as the other, then they will not have right angles because they do not intersect at a single point.
- Two lines can only be parallel if all of their points lie on or within one plane or all lie on or within two planes that are perpendicular to each other (i.e., when one goes up and down, then so does the other).
- Two lines can only be parallel if they do not intersect at any point.
- Two lines can only be parallel if the sum of their lengths is equal to the length of a third line (if one goes up and down, then so does the other).
- Two lines can only be parallel if the angles formed by them are equal (180 degrees).
- Two lines can only be parallel if they do not intersect at any point.
- If a line is perpendicular to another line, then they will have right angles because they intersect at a single point.
- If two lines are perpendicular to each other, then they will have right angles because they intersect at a single point.
Conclusion
Now, you know what a parallelogram is, why parallelograms do not have right angles when parallelograms have right angles and the reason why parallelograms do not have right angles. All you have to do now is to practice these concepts and make them part of your daily geometry routine. Once you have mastered these concepts, you can move on to the next level of geometry.
