Question

In a quadrilateral ABCD, AB is the shortest whereasCD is the longest side. Prove AngleA>AngleC. Plz attach figure

Answer 1

Proof :-

In quad ABCD ,We can find two triangles - ΔADC & ΔABC 

→ Now , In ΔADC

∠DAC   > ∠ DCA { Angles opposite to smaller side is smaller } → 1st Equation

→Now , In ΔABC 

∠BAC  > ∠ ACB { Angles opposite to smaller side is smaller } → 2nd Equation

Let us now add the first two equations respectively ,

→ ∠ DAC + ∠BAC   >   ∠DCA  + ∠ ACB

→ ∠ BAD   > ∠ BCD 

⇒ Hence proved that ∠ A  > ∠ C