Question

ABCD is a rectangle in which diagonal AC bisects angle A as well as single stage show that first ABCD is a square​

Answer 1

Answer:

Given : ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C.  

To Prove :  

(i) ABCD is a square.  

(ii) Diagonal BD bisects ∠B as  

well as ∠D.  

Proof : (i) In ∆ABC and ∆ADC, we have  

∠BAC = ∠DAC [Given]  

∠BCA = ∠DCA [Given]  

AC = AC  

∴ ∆ABC ≅ ∆ADC [ASA congruence]  

∴ AB = AD and CB = CD [CPCT]  

But, in a rectangle opposite sides are equal,  

i.e., AB = DC and BC = AD  

∴ AB = BC = CD = DA  

Hence, ABCD is a square Proved.  

(ii) In ∆ABD and ∆CDB, we have

AD = CD  

AB = CD [Sides of a square]  

BD = BD [Common]  

∴ ∆ABD ≅ ∆CBD [SSS congruence]  

So, ∠ABD = ∠CBD  

∠ADB = ∠CDB  

Hence, diagonal BD bisects ∠B as well as ∠D Proved

HOPE THIS HELPED YOU!

Answer 2

Answer:

Given :- Abcd is a rectangle. AC bisects Angle A

To prove :- Abcd is a square