Subscribe to our YouTube channel for the latest videos, updates, and tips.
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
-
Terms Related to Simple Interest | Simple Interest Formula | Principal
Jun 18, 25 02:57 PM
In terms related to simple interest we will learn all the terms related to simple interest. The terms related to simple interest are Interest, Principal, Amount, Simple Interest, Time or period of tim… -
Introduction to Simple Interest | Definition | Formula | Examples
Jun 18, 25 01:50 AM
In simple interest we will learn and identify about the terms like Principal, Time, Rate, Amount, etc. PRINCIPAL (P): The money you deposit or put in the bank is called the PRINCIPAL. -
5th Grade Profit and Loss Percentage Worksheet | Profit and Loss | Ans
Jun 18, 25 01:33 AM
In 5th grade profit and loss percentage worksheet you will get different types of problems on finding the profit or loss percentage when cost price and selling price are given, finding the selling pri… -
Worksheet on Profit and Loss | Word Problem on Profit and Loss | Math
Jun 18, 25 01:29 AM
In worksheet on profit and loss, we can see below there are some different types of questions which we can practice in our homework. -
Calculating Profit Percent and Loss Percent | Profit and Loss Formulas
Jun 15, 25 04:06 PM
In calculating profit percent and loss percent we will learn about the basic concepts of profit and loss. We will recall facts and formula while calculating profit percent and loss percent. Now we wil
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.