Question

ABCD is a rhombus. Show that diagonal AC bisects Z A as well as C and diagonal BD bisects ZB as well as D.

plz anyone answer
class 9th Quadrilateral......

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Answer 1

Answer:

Given,

ABCD is a Rhombus

In a Rhombus all sides are equal.

Then, Take a ∆le ABC

In which AB = AC.

So,

Angle BAC = Angle BCA......... equation (1)

And In ∆le ADC

In which AD = AC

So,

Angle DAC = Angle ACD......... equation (2)

From (1) & (2)

we come to know that...

Diagonal "AC" bisects Angle A and Angle C

Similarly.

BD bisects Angle B and Angle D...

Step-by-step explanation:

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Answer 2

Answer:

$given -$

ABCD is a rhombus

$to \: prove -$

Diagonal AC bisects ZA as well as C and diagonal BD as well as D

$solution -$

In rhombus all side are equal and diagonols are different but intersect at 90

0

]

⇒AB=BC=CD=DA

⇒AC⊥BD

InΔABC

⇒AB=BC

⇒∴∠CAB=∠ACB

⇒AO=OC

∴∠ABO=∠CBO

and simillarly in ΔADC

⇒AD=DC

⇒AO=OC

∴corresponding angle are equal

⇒∠DAC=∠DCA

and∠CDO=∠ADO

Hence,AC bisect ∠A and ∠C and BD bisects ∠B and ∠D

$thank \: you$

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