Question

AB and CD are respctively the small est and longest sides of quadrilaterial ABCD.show that [<A><Cand<B><D​

Answer 1

Answer:

will you please tell me first what we have to show in this question

Answer 2

SOLUTION

given,

ABCD is quadrilateral where AB and CAD are respectively shortest and longest side.

To prove: <A > <C and <B > <D

Construction: join AC and BD.

Proof: In triangle ABC, AB is the shortest side.

therefore, BC>AB

<BAC > <ACB ------- (1) [ Angles opposite to longer side is greater]

Again,

In triangle ADC, CD is the longest side.

therefore, CD>AD

<DAC > <ACD --------- (2) [ Angle opposite to longer side is greater]

NOW,

Adding 1 and 2, we get

<BAC + <DAC > <ACB + <ACD

= <BAD > <BCD

I.e =<A > <C

Similarly, we can prove that :-

<B > <D