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Question

Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).



A

1:2

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B

2:1

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C

1:1

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D

None of the above

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Solution

The correct option is C

1:1


D is the midpoint of AB. A line segment DE is drawn which meets AC in E and is parallel to the opposite side BC.

BCFD is a parallelogram    DF || BC and CF || BD

CF = BD {opposite sides of parallelogram are equal}

CF = DA {Since BD = DA given}

In  ADE and  CFE

AD = CF

DAE = ECF {Alternate angles}

ADE = EFC {Alternate angles}

 ADE ≡  CFE

AE = EC {Corresponding parts of congruent triangles are equal}

AE: EC = 1: 1


Mathematics

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