In this post, we will discuss theorem 7.8 class 9 Maths which is related to Chapter 7 Triangles Class 9 Mathematics. After understanding theorem 7.8, you can solve the exercise questions given in the NCERT book of Class 9 Maths.
Solve Theorem 7.8 Class 9
The sum of any two sides of a triangle is
greater than the third side.
Given
A triangle ABC
To prove
(i) BA + AC >BC
(ii) AB + BC > AC
(iii) BC + AC> AB
Construction
Produce BA to D such that AD=AC. Join CD
Proof
In ∆ACD
AD= AC (by construction)
⟹ ∠ACD=∠ADC (angles opposite to equal sides are equal)
∠BCA+ ∠ACD+ ∠ADC
⟹ ∠BCD> ∠ADC
⟹ BD>BC (in a triangle, the side opposite to the greater angle is longer)
⟹ AB+AD>BC(∵BD=AB+AD)
AB+ AC > BC (∵AD=AC,by construction)
Hence, AB+ AC > BC
Similarly, we can prove that AB+BC>AC and BC+AC>AB
Related Topics
1. Theorem 7.6
2. Theorem 7.7
Nice
ReplyDelete