4. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Fig.). Show that \small \angle A>\angle C and \small \angle B>\angle D.

              

Answers (1)

                                           

Consider \Delta ADC in the above figure : 

AD\ <\ CD          (Given)

Thus         \angle CAD\ > \angle ACD                   (as angle opposite to smaller side is smaller)      

Now consider \Delta ABC,

We have :                BC\ > AB

and                            \angle BAC\ > \angle ACB

Adding the above result we get,

                       \angle BAC\ +\ \angle CAD > \angle ACB\ +\ \angle ACD

or                                                     \small \angle A>\angle C

Similarly, consider \Delta ABD,

we have               AB\ <\ AD  

Therefore               \angle ABD\ > \angle ADB

and in  \Delta BDC  we have,

                                             CD\ >\ BC

and                                \angle CBD\ >\ \angle CDB

from the above result we have,

                                \angle ABD\ +\ \angle CBD\ >\ \angle ADB\ +\ \angle CDB

or                                                                \small \angle B>\angle D

Hence proved.

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions