Question

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ABCD is a quadrilateral in which all four sides are equal. Show that both pairs of
opposite sides are parallel.​

Answer 1

Step-by-step explanation:

Draw a rhombus ABCD ,

Join BD and AC

In ∆ AND and ∆ BCD

• AD = CD ( : . given )
• AB = BC ( :. given )
• BD = BD ( :. common )

By SSS Congruence rule

• ∆ ACD ≈ ∆ ACB

By CPCT ,

• angle ACB = angle DAC

These are the angles formed when the transversal AC joins AD and BC.

They are alternate interior angles

• AD // BC
• AD = BC ( :. given )

Similarly we can find,

• AB // CD
• AB = CD