Can a Triangle have Any Parallel Sides?

Does a Triangle have Perpendicular Sides? What is a Pythagorean Theorem for a Right-Angle Triangle? What is the Formula for The Base of Isosceles Triangle? How to find out the Third Side of the Triangle?
can a triangle have any parallel sides

A triangle has three angles that add up to 180 degrees because one exterior angle equals the sum of the other two opposite angles in a triangle. In other words, the other two angles in a triangle combine with the third angle to make a 180-degree angle. Have you ever wondered, can a triangle have any parallel sides and does a triangle have perpendicular sides? These side and angle concepts have a lot to do with rectangles, pentagons, hexagons, and all those multi-sided shapes that are referred to as polygons. Further, you will know why a triangle always stretches a straight line from another line and how many parallel sides can a triangle have.

1. Can a Triangle have Any Parallel Sides?

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Photo by Shubham Dhage on Unsplash

If you have a creative mind, think about how many parallel sides can a triangle have. Well, it is a tricky concept for an algebraic construction, since it is related to the polygon family. Before we find out how can a triangle have any parallel sides, we need to understand the angles of a triangle. The lines need to intersect to form 180 degrees. The triangle is a closed body shape that has three sides. The lines of a triangle connect each other. So, the answer to the above question is NO.

This is the reason there couldn’t be any parallel sides. The lines are parallel if they sit at the same angle and do not intersect. A triangle can never have any parallel sides because the sum of angles must be 180 degrees so that sides will intersect. (See How Many Vertices Does a Triangle Have)

2. Does a Triangle have Perpendicular Sides?

Perpendiculars have a 90-degree angle. A triangle can have perpendicular sides if it is a right-angled triangle. Any side whose corresponding angle is 90 degrees is called a perpendicular side. For shapes like hexagons or octagons, they do not have any perpendicular sides. The reason is that they have equal angles and sides and thus, they cannot be perpendicular. The following are some of the shapes that have perpendicular sides:

  • The most common shapes which have perpendicular sides are squares and rectangles.
  • The right-angled triangle also has perpendicular sides. It is called a right triangle because it has a right-angle for one of its three angles, where the angle of the line is 90 degrees. (See Why is Mathematical Concept Important?)

3. How Many Parallel Sides Can a Triangle have?

A triangle does not have any parallel sides since it is a polygon. Parallel lines do not cross each other, whether you make them too long or too short. They have flat, two-dimensional shapes with straight edges. 

4. Which Shape has Parallel Sides?

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Besides learning whether can a triangle have any parallel sides or not, here are the following shapes that have parallel sides.

  • Rectangle
  • Square
  • Parallelogram
  • Trapezoid
  • Hexagon
  • Octagon

You now know how many parallel sides can a triangle have, none. But do you know that a regular octagon has 4 pairs of parallel sides? To know more about it, check out What is a Polygon Shape?

5. How Many Types of Triangles are There?

There are three types of triangles.

  • Equilateral Triangles – The length and angles of the three sides are equal.
  • Isosceles Triangles – It has two sides of equal length, two equal angles and another side is unequal.
  • Scalene Triangle – All the sides here have different lengths and angles. (See What Shapes have 4 Sides?)

6. What is a Pythagorean Theorem for a Right-Angle Triangle?

Pythagorean Theorem: can a triangle have any parallel sides 4
From cuemath.com

The Pythagorean Theorem finds the length of the hypotenuse of a right-angle triangle. It was formulated by a Greek mathematician named Pythagoras. He says if you have a triangle with sides AB, BC, and CA, BC is the hypotenuse. If you have the value of two lengths, you can always use algebra and square roots to find out the missing side.

The formula is BC2AB2 + AC2. The square of the hypotenuse is equal to the sum of the squares of the other two sides. (See What are the Types of Functions?)

7. What is The Formula for the Base of Isosceles Triangle?

If the length of the other two sides and perimeter of an isosceles triangle are known, the base of the triangle can be found using this formula,

The formula is b = P − 2a,

P= Perimeter of the triangle, and a = length of other sides. Also, check out what is a Circle Degree Chart?

8. How to find out the Third Side of the Triangle?

There are some more concepts of trigonometry that you need to know. Use Pythagoras Theorem to find the other side if it is a right-angle, use the area formula if it is an isosceles triangle, and use the law of cosines and sines if you know the angles. This helps you find the third side of a triangle. (See How many Sides does a Pentagon have?)

9. How Many Degrees are There in a Triangle?

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Photo By Antoni Shkraba on Pexels

If you again ask, can a triangle have any parallel sides? Well, no because its angle always sums to 180°. We can check this out by adding the interior angles of a triangle. 

10. Why is It called a Triangle?

Every triangle has three sides and three angles. They also vary in terms of shapes and sizes. Closed shapes are referred to as polygons and can be called by different names. A triangle has three closed sides and tri refers to three, hence the name triangle. Pascal discovered the triangle. In 1653, he organized and found that it could be used in numerous ways. 

So, you got answers to can a triangle have any parallel sides and if not, then does a triangle have perpendicular sides? Hope you understood that how many parallel sides can a triangle have is not a valid question too.  (See How long is 8 inches Compared to an Object?)

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