Question

in a parallelogram ABCD, E and F are the mid-points of sides AB andCD respectively. Show
that the line segments AF and EC trisect the diagonal BD.
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Answer 1

INSTRUCTIONS- // MEANS PARALLEL IN THIS QUESTION

Step-by-step explanation:

CD||AB and CD=AB

Multiply both sides of both the equations by 1/2

1/2CD // 1/2AB and 1/2CD=1/2AB

FC//AE and FC=AE. (because F and E are respectively the mid points of CD and AB)

Therefore AECF is a parallelogram

In triangle CQD,

PF //CQ and F is the mid point of CD then P is also the mid point of DQ (from mid point theorem)

that means DP=PQ. (suppose this is equation 1)

Similarli in triangle ABP, PQ=BQ. (Suppose this is equation 2)

From equation 1&2, DP=PQ=BQ

HENCE line segments AF and CE trisect the diagonal BD

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