Question

abcd is a parallelogram what special name will you give it if they following additional facts are known?
i) AB=AD
ii)angleA = 90°
AB=AD and DAB=90°
pls answer step by step​

Answer 1

Answer:

Given: In parallelogram ABCD, the diagonals AC & BD are equal & perpendicular to each other.

∠DOC=∠COB=∠BOA=∠AOD=90

o

We know that diagonals of a parallelogram bisect each other.

So OA=OC=OB=OD ---(1)

In △AOD&△AOB,

OA=OA [ Common side ]

∠BOA=∠AOD=90

o

[ Given ]

OD=OA [ from (1) ]

So △AOD≅△AOB [ By SAS Rule of Congruency ]

Therefore AD=AB.

So AB=BC=CD=DA [ Since ABCD is a parallelogram ] ---(2)

In △ADB & △BCA,

AB=AB [ Common side ]

AD=BC [ from (2) ]

AC=BD [ given ]

Therefore △ADB≅△BCA [ By SSS Rule of Congruency ]

So ∠DAB=∠CBA

Now adjacent angles in a parallelogram are supplementary.

So ∠DAB+∠CBA=180

o

⇒2∠DAB=2∠CBA=180

o

⇒∠DAB=∠CBA=

2

180

o

⇒∠DAB=∠CBA=90

o

Similarly we can prove that ∠ADC=∠BCD=90

o

So in the given parallelogram, all sides are equal & each interior angle is 90

o

.

Therefore parallelogram ABCD in which diagonals are equal & are perpendicular to each other is definitely a Square.

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Answer 2

Answer:

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Step-by-step explanation:

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