Question

ABCD is a rhombus show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects Angle B as well as angle d​

Answer 1

Answer

Step-by-step explanation:

We can solve the problem by using properties of triangle as well as rhombus.

Hope it helps you

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Answer 2

Answer:

Given :-

ABCD is a rectangle in which diagonal AC bisects

angle A as well as angle C.

To prove :-

I) ABCD is a square.

ll) Diagonal BD bisects angle B as well as angle D.

Proof :-

I) In ∆ABC and ∆ADC, we have

angle BAC = angle DAC

angle BCA = angle DCA

AC = AC ( common)

therefore, ∆ABC congruent ∆ADC[ASA]

therefore, AB = AD and CB = CD [cpct]

but in rectangle opposite sides are equal,

i.e, AB=DC and BC=AD

therefore AB=BC=CD=DA

Hence, ABCD is a square ⬛ proved

ll) In ∆ABD and ∆CDB,

AD=CD

AB=CD

BD=BD

THEREFORE, ∆ABD congruent ∆CBD (SSS)

so, angle ABD= angle CBD

angle ADB= angle CDB

HENCE, diagonal BD bisects angle B as well as angle D.

Proved