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 DC and AD BC. Now let us discuss some theorems |
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] ADP = QBC [ Alternate interior angles whne AD || BC and BD is the transversal] DP = QB [ Given] [ SAS criteria of congruence] Part (1) Proved AP = CQ [ C.P.C.T.] Part (2) Proved In AB = CD [ opposite sides of a parallelogram] ABQ = CDP [ Alternate interior angles whne AB || CD and BD is the transversal] BQ = DP [ Given] [ SAS criteria of congruence] Part (3) Proved AQ = CP [ C.P.C.T.] Part (4) Proved Now in the quadrilateral both the opposite pair of sides are equal. APCQ is a parallelogram Part (5) Proved |
The perimeter of a parallelogram is 180 cm. One side exceeds the other by 30 cm. The adjacent sides of the parallelogram are ____________ | |||
Right Option : B | |||
View Explanation |
If ABCD is a parallelogram, then <A - <C is : | |||
Right Option : B | |||
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 |
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Abhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
My experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
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Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...