Question

ABCD is a quadrilateral.
Prove that (AB + BC + CD + DA) > (AC + BD).​

Answer 1

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To show that

ABCD is a quadrilateral.

Prove that (AB + BC + CD + DA) > (AC + BD).

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Step by step explanation:

Construction:Join A To C and B To D

Now ,we get AC and BD as diagonal and

We get four triangles ∆ABC ,∆BDC,∆ACD &∆ABD

=>Sum of two sides of a triangle is greater than the third side.

• So,AB+BC >AC
• CD+AD>AC
• AB+AD>BD
• BC+CD>BD

Adding all above :-

=>2(AB+BC+AC+AD)>2(AC+BD)

=>2(AB+BC+CA+AD)>2(AC+BD)

=>(AB+BC+CA+AD)>(AC+BD)

$\bold{\red{∴(AC+BD)<(AB+BC+CA+AD)}}$