Home
Class 9
MATHS
Theorem 8.3 : If each pair of opposite s...

Theorem 8.3 : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Text Solution

Verified by Experts


In `/_\ABC` and `/_\CDA`
It is given that, `AB=CD`
It is given that, `AD=BC`
`AC` is the common side
. So, by SSS condition both the triangles are congruent.
Then, by common property of common triangles we get,
...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

Theorem 8.5 : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel.

Complete each of the following statements by means of one of those given in brackets again each: If one pair of opposite sides are equal and parallel, then the figure is ............... (parallelogram, rectangle, trapezium) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is .............. (square, rectangle, trapezium) A line drawn from the mid-point of one side of a triangle .................. another side intersects the third side at its mid-point. (perpendicular to, parallel to, to meet) If one angle of a parallelogram is a right angle, then it is necessarily a .................... (rectangle, square, rhombus) Consecutive angles of parallelogram are ...................... (supplementary, complementary) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily (rectangle, parallelogram, rhombus) if opposite angles of a quadrilateral are equal, then it is necessarily a ................... (parallelogram, rhombus, rectangle) If consecutive sides of a parallelogram are equal, then it is necessarily a ............. (kite, rhombus, square)

If two opposite sides of a cyclic quadrilateral are equal; then the other two sides are parallel.

Theorem 8.2 : In a parallelogram, opposite sides are equal.

Theorem 8.7 : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Theorem 10.12 : If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

In a parallelogram opposite sides are equal

State whether the statements are true (T) or (F) false. If opposite angles of a quadrilateral are equal, it must be a parallelogram.