ABCD is a quadrilateral in which all four sides are equal show that both pairs of opposite sides are parallel
Answers
Answered by
14
Given: A quadrilateral with all sides equal.
To prove that the opposite pairs of sides are parallel.
Construction. Draw a rhombus ABCD. Join BD.
Proof: In triangles ABD and BCD
AD=CD [given]
AB=BC [given]
BD is common
So triangles ABD and BCD are congruent.
<ADB = <CBD and so alternate angles. Therefore, BD is a transversal and so AD is parallel to CB.
Again, <ABD = <CDB and so alternate angles. Therefore, BD is a transversal and so AB is parallel to CD.
Hence opposite pairs of sides are parallel.
QED.
To prove that the opposite pairs of sides are parallel.
Construction. Draw a rhombus ABCD. Join BD.
Proof: In triangles ABD and BCD
AD=CD [given]
AB=BC [given]
BD is common
So triangles ABD and BCD are congruent.
<ADB = <CBD and so alternate angles. Therefore, BD is a transversal and so AD is parallel to CB.
Again, <ABD = <CDB and so alternate angles. Therefore, BD is a transversal and so AB is parallel to CD.
Hence opposite pairs of sides are parallel.
QED.
Similar questions
History,
5 months ago
English,
11 months ago
Social Sciences,
11 months ago
Math,
1 year ago
English,
1 year ago