Step by step explanation:
if ABCD is a quadrilateral is AB + BC + CD + DA
is lesser than 2 AC + 2 BD?

Question

Step by step explanation: if ABCD is a quadrilateral is AB + BC + CD + DAis lesser than 2 AC + 2 BD?

Answer

Explanation:

Given:
Given that ABCD is a quadrilateral, and AB + BC + CD + DA is lesser than 2AC + 2BD.
To prove:
We need to prove that AB + BC + CD + DA < 2ac='' +='' />
Proof:
Let's consider the quadrilateral ABCD:
- Let AB = a
- Let BC = b
- Let CD = c
- Let DA = d
Applying Triangle Inequality Theorem:
According to the Triangle Inequality Theorem, in any triangle, the sum of the lengths of any two sides is always greater than the length of the third side.
Using Triangle Inequality Theorem in Quadrilateral ABCD:
In quadrilateral ABCD,
- AB + BC > AC
- BC + CD > BD
- CD + DA > AC
- DA + AB > BD
Adding the Inequalities:
Adding the above inequalities, we get:
AB + BC + CD + DA > AC + BD
Given Inequality:
Given that AB + BC + CD + DA < 2ac='' +='' />
Conclusion:
From the above inequalities, we can conclude that AB + BC + CD + DA is indeed less than 2AC + 2BD.