Properties of Parallelogram
Properties of Parallelogram
PROPERTIES OF PARALLELOGRAM: A quadrilateral is a prallelogram if its both pairs of opposite sides are parallel to each other. In fig., quadrilateral ABCD is a prallelogram, because AB |  |
Theorem 1: A diagonal of a prallelogram divides it into two congruent triangles.
Theorem 2: In parallelogram, opposite sides are equal.
Theorem 3: The opposite angles of a parallelogram are equal.
Theorem 4: The diagonals of a parallelogram bisect each other.
Theorem 5: In a parallelogram, the bisectors of any two consecutive angles intersect at right angle.
Theorem 6: If diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angles. Also, prove that it is a rhombus.
Theorem 7: The angle bisectors of a parallelogram form a rectangle.
ILLUSTRATION: In a parallelogram ABCD two points P and Q are taken on the diagonal BD such that DP = BQ. Show that
(1) (2) AP = CQ (3)
(4) AQ= CP (5) APCQ is a parallelogram
Solution: In AD = CB [ opposite sides of a parallelogram] DP = QB [ Given] In AB = CD [ opposite sides of a parallelogram] BQ = DP [ Given] Now in the quadrilateral both the opposite pair of sides are equal.
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In the figure given below AP and CQ are perpendiculars to the diagonal BD of a parallelogram. Then
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| Right Option : A | |||
| View Explanation |
The diagonals of a parallelogram ABCD intersect at O. If <BOC=90 and <BDC 50 ,then <OAB is : | |||
| Right Option : B | |||
| View Explanation | |||
If ABCD is a parallelogram, then <A - <C is : | |||
| Right Option : B | |||
| View Explanation | |||
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