# q1. in the adjoining figure, abcd is a trapezium in which ab//dc..p and q are mid points of ad and bc respectively. dq and ab when produced meet at e.prove that (1)dq=qe (2) ar=rc (3) pr//abq2. point m and n divide the side ab of a triangle abc into three equal parts. line segments mp and nq are both parallel to bc and meet ac in p and q respectively.prove that p and q divide ac in three equal partsq3. if two parralelograms pqad and pqbc are on the opposite sides of pq, prove that abcd is a paralleleogramq4. if a line is parallel to the base of a trapezium and bisects one of the non parallel sides then prove that it bisects either diagonal of the trapeziumq5. points a and b are on the same sides of the line l. ad is perpendicular to l and be is perpendicular to l in d and e respectively if c is the mid point of ab , prove that cd = ce

Dear Student, Anamika,

due to paucity of time it would not be possible for us to answer all of your queries here.

we are providing solution of one of your query. please try the remaining problems yourself and

if you face any difficulty do get back to us.

given: ABCD is a trapezium, such that

and Q is the mid point of BC.

TPT: DQ = QE

Proof:

in the triangles BQE and CQD,

BQ = QC [since Q is the mid point of BC]

[vertically opposite angles]

[alternate interior angles]

therefore by ASA congruency

therefore by CPCT, DQ = QE.

since either the position of  point R or figure is not mentioned here, so please again go through the question and do get back to us.

hope this helps you.

cheers!!

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