Download Article Download Article
Determining if three side lengths can make a triangle is easier than it looks. All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle. X Research source Go to source
wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 32 people, some anonymous, worked to edit and improve it over time. This article has been viewed 865,199 times.
Updated: August 23, 2022
Article Rating: 72% - 105 votes
Thanks to all authors for creating a page that has been read 865,199 times.
Consider two triangles $\triangle abc$ and $\triangle def$ such that $ab=de$ and $ac=df$.Also area of $\triangle abc$ is equal to area of $\triangle def$.Now draw $cm$ perpendicular to $ab$ and $fn$ perpendicular to $de$.$ab$ and $de$ are equal and area of triangles is also equal so $cm$ should be equal to $fn$.Now $\triangle amc$ and$\triangle dnf$ are congruent by right angle triangle congruence(since hypoteneous $ac$ and $df$ are equal).therefore $\angle bac$ is equal to $\angle edf$.Now in $\triangle abc$ and $\triangle def$ by SAS both $\triangle abc$ and $\triangle def$ are congruent so $bc=ef$.I don't know where i am wrong.
edit:Please read my proof and point out what's wrong$\endgroup$ 2
Triangle is a closed figure which is formed by three line segments. It consists of three angles and three vertices. The angles of triangles can be the same or different depending on the type of triangle. There are different types of triangles based on line and angles properties.
Properties of a Triangle:
1. Each triangle has 3 sides and 3 angles.
2. Sum of all the angles of triangles is 180°
3. Perimeter of a triangle is the sum of all three sides of the triangle.
4. A triangle has 3 vertices.
Types of Triangles based on line Properties
Scalene Triangle: Scalene Triangle is a type of triangle in which all the sides are of different lengths. All the angles of a scalene triangle are different from one another.
Isosceles Triangle: Isosceles Triangle is another type of triangle in which two sides are equal and the third side is unequal. In this triangle, the two angles are also equal and the third angle is different.
Right-angled Triangle: A right-angled triangle is one that follows the Pythagoras Theorem and one angle of such triangles is 90 degrees which is formed by the base and perpendicular. The hypotenuse is the longest side in such triangles.
Equilateral Triangle: An equilateral triangle is a triangle in which all the three sides are of equal size and all the angles of such triangles are also equal.
Finding Third Side of a Triangle given Two Sides
Lets assume that the triangle is Right Angled Triangle because to find a third side provided two sides are given is only possible in a right angled triangle.
We know that the right-angled triangle follows Pythagoras Theorem
According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side.
Using the above equation third side can be calculated if two sides are known.
Example: Suppose two sides are given one of 3 cm and the other of 4 cm then find the third side.
Question 1: Find the measure of base if perpendicular and hypotenuse is given, perpendicular = 12 cm and hypotenuse = 13 cm.
Question 2: Perimeter of the equilateral triangle is 63 cm find the side of the triangle.
Question 3: Find the measure of the third side of a right-angled triangle if the two sides are 6 cm and 8 cm.
Question 4: Find whether the given triangle is a right-angled triangle or not, sides are 48, 55, 73?
Question 5: Find the hypotenuse of a right angled triangle whose base is 8 cm and whose height is 15 cm?
Article Tags :