Question

For any triangle ABC, the true statement is:
A) \[A{C^2} = A{B^2} + B{C^2}\]
B) \[AC = AB + BC\]
C) \[AC > AB + BC\]
D) \[AC < AB + BC\]

Answer 1

Hint:
Here we will first draw the diagram of the triangle. Then we will form the condition from the basic property of the sides of the triangle and then select the required condition according to the given option.

Complete step by step solution:
First, we will draw a triangle ABC to get the correct relationship of the sides of the triangle.

We know this property of the triangle that the sum of any two sides of the triangle is always greater than the third side of the triangle.
So we can write the above property as
\[\begin{array}{l}AB + BC > AC \\ AB + AC > BC \\ BC + AC > AB\end{array}\]
So from the above formed conditions we have the first condition given as an option. So the required condition is
\[AB + BC > AC\]
We can write it as
\[AC < AB + BC\]
Hence, the true statement is \[AC < AB + BC\].

So, option D is the correct option.

Note:
A triangle is a polygon with three edges or sides and three vertices. Side is one of the straight line segments which are used to construct or draw a polygon. When two or more lines cross each other in a plane, they are called intersecting lines and the point where these lines intersect is called a Point of Intersection or vertex. In the equilateral triangle all the sides are equal and also all the angles of the triangle are equal. In the right angled triangle two sides of the triangle are perpendicular to each other. Hypotenuse is the longest side of the right angled triangle.