Question

ABCD is a quadrilateral in which all the four angles and equal show that a b abs parallel to CD and a b is parallel to BC justify

Answer 1

Q) ABCD is a quadrilateral with all the sides equal. Show that AB || CD and AD || BC.

Solution:-

Given,
ABCD is a quadrilateral
Angles A=B=Ç=D
To Prove,
AB || CD and AD || BC

Proof:- Here,
angle A+B+Ç+D=360° [angle sum property of quadrilaterals]
=>A+A+A+A=360°
=>4A=360°
=>A=90° ……[equation 1]

Again, angle A+B=180°
Therefore, angles A and B are linear
And also they are adjacent.
Therefore, AD || BC because there interior angles A and B add up to 180°.

Similarly, angle A+D=180°
Therefore, angles A and D are linear
And also they are adjacent.
Therefore, AB || CD because there interior angles A and B add up to 180°.

Therefore, it is proved that AB ||CD
And AD || BC.

Answer 2

Answer:

HERE OS YOUR ANSWER

BADI MEHNAT LAGI YAR PLS.

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Explanation:

ANSWER

ABCD is a quadrilateral with four equal sides

If the sides are equal they will produce four equal angles

Hence each angle will be 90 degree (Sum of interior angles is 360 degree)

Hence ABCD is considered as a SQUARE

AC and BD are joined which meet at O

AC and BD are diagonals , which bisect interior angles.

Angle BAD is bisected by AC

Angles BAC = DAC

Angle BCD is bisected by AC

Angles ACD = BCA

Since, BAD = BCD = 90°

Angles BAC = DAC = Angles ACD = BCA

BAC = ACD

They are also interiorly alternate to each other.

So by converse theorem,

AB is parallel to CD

Similarly Angles ABD = CBD = ADB = CDB (when BD is the bisector)

CBD = ADB

They are also interiorly alternate to each other.

So by converse theorem,

AD is parallel to BC

Hence opposite pairs of sides are parallel to each other