# Sum of the Four Sides of a Quadrilateral Exceeds the Sum of the Diagonals

Here we will prove that in any quadrilateral the sum of the four sides exceeds the sum of the diagonals.

Solution:

Given: ABCD is a quadrilateral; AC and BD are its diagonals.

To prove: (AB + BC + CD + DA) > (AC + BD).

Proof:

 Statement Reason 1. In ∆ADB, (DA + AB) > BD. 1. Sum of the two sides of a triangle is greater than the third side. 2. In ∆ABC, (AB + BC) > AC. 2. As above. 3. In ∆BCD, (BC + CD) > BD. 3. As above. 4. In ∆CDA, (CD + DA) > AC. 4. As above. 5. 2(AB + BC + CD + DA) > 2(AC + BD). 5. Adding the equations in statements 1, 2, 3 and 4. 6. (AB + BC + CD + DA) > (AC + BD). (Proved) 6. Cancelling the common factor 2.

From Sum of the Four Sides of a Quadrilateral Exceeds the Sum of the Diagonals to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

Mar 02, 24 05:31 PM

The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

2. ### Subtraction of Fractions having the Same Denominator | Like Fractions

Mar 02, 24 04:36 PM

To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

3. ### Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

Mar 02, 24 03:32 PM

To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

4. ### Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

Mar 01, 24 01:42 PM

In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…