Class 8th Parallel lines pls solve both the question
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ABCD is a quadrilateral in which all four sides are equal. How would you show that both pairs of the opposite sides are parallel?
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Tarkeshwar Prasad, Teacher at Loreto Convent
Answered Feb 18
In quadrilateral ABCD,
AB=BC=CD=DA ……(1) (given)
We join vertex A &C.
In ∆ABC & ∆CDA,
AB = CD (from equation 1)
BC = DA (from equation 1)
AC = CA (common)
=> ∆ABC is congruent to ∆CDA (by S.S.S.)
Therefore, Angle BAC = Angle DCA (by C.P.C.T)
Hence, AB // DC …(2)
Similarly, Angle ACB = Angle CAD (by C.P.C.T)
Hence, BC // AD …(3)
From equation (2) & (3) we get that AB // DC and BC // AD
Answer
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3 ANSWERS

Tarkeshwar Prasad, Teacher at Loreto Convent
Answered Feb 18
In quadrilateral ABCD,
AB=BC=CD=DA ……(1) (given)
We join vertex A &C.
In ∆ABC & ∆CDA,
AB = CD (from equation 1)
BC = DA (from equation 1)
AC = CA (common)
=> ∆ABC is congruent to ∆CDA (by S.S.S.)
Therefore, Angle BAC = Angle DCA (by C.P.C.T)
Hence, AB // DC …(2)
Similarly, Angle ACB = Angle CAD (by C.P.C.T)
Hence, BC // AD …(3)
From equation (2) & (3) we get that AB // DC and BC // AD
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