Today, we will discuss theorem 8.3 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.3, you can solve the exercise questions given in the NCERT book of Class 9 Maths.
Theorem 8.3 Class 9
If each pair of opposite sides of a quadrilateral is
equal, then it is a parallelogram.
Given
ABCD is a quadrilateral in which opposite sides are equal.
AB=DC and BC=AD
To Prove
ABCD is a parallelogram
AB∥DC and BC∥AD
Construction
Join AC
Proof
In ∆ABC and ∆CDA
AC=AC (common sides)
AB=DC (given)
BC=AD (given)
∆ABC≅∆CDA (By SSS congruence rule)
Then ∠BAC=∠ACD
And ∠BCA=∠CAD
But these are pairs of alternate angles (By CPCT)
∴ AB∥DC and BC∥AD
Hence ABCD is a parallelogram. Hence proved
Related Topics
1. Theorem 8.4
2. Theorem 8.2
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