The pair of opposite sides of a quadrilateral are equal prove that its opposite sides are parallel
Answers
Answer:
ABCD is a quadrilateral
given_ opp. sides equal
let AB=CD opp. sides
let AD=BC " "
construction- join BD
in triangle ABD and triangle BDC
AB=CD given
AD=BC "
BD= BD common side
hence triangle ABD congruent to triangle BCD
by C.P.C.T angle ABD= angle BDC
hence AB parallel to CD
similarly BC paralled to AD
Answer:
To prove:- AB ll CD and AC ll BD
Construction-Join BD
Step-by-step explanation:
It is given a quadrilateral.Means, its all sides would be equal.
So, AB=CD. ........(i)
also, AD=BC. .......(ii)
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In triangles ABD and BDC,
AB=CD. [From (i)]
AD=BC. [From (ii)]
BD=BD. [Common]
Therefore, Triangle ABD is congruent to Triangle BDC. [SSS Congruency]
:Where, angle ABD = angle BDC. (iii) [CPCT]
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But, in equation (iii), the angles are a pair of alternate interior angles on line AB and CD,when a tranversal BD intersects them
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Hence, AB ll CD.
similarly, AD ll BC. PROVED