SOLUTION: Can you prove if the quadrilateral is a parallelogram then opposite sides of a quadrilateral are congruent?

Question 62873: Can you prove if the quadrilateral is a parallelogram then opposite sides of a quadrilateral are congruent?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Can you prove if the quadrilateral is a parallelogram then opposite sides of a quadrilateral are congruent?
LET ABCD BE THE QUADRLATERAL WITH
AB||CD AND
BC||AD
JOIN AC
IN TRIANGLES ABC AND ADC,
AC=AC
ANGLE CAB = ANGLE ACD.... ALTERNATE ANGLES WITH AB||CD AND
AC BEING THE TRANSVERSAL
ANGLE ACB = ANGLE CAD ....ALTERNATE ANGLES WITH AD||BC AND
AC BEING THE TRANSVERSAA
HENCE THE 2 TRIANGLES ARE CONGRUENT BY AAS THEOREM
HENCE
AB = CD...... AND
BC = AD
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