íí) In the triangle ABC , through the midpoint D of AB, if a line segment DE parallel to BC is drawn, which intersects the side AC at the point E then (a) AE =1/3 AC (b) AE =1/2 AC (c) AE = 1/4 AC (d) AE =2/3 AC What is the correct answer of this MCQ?
Answers
Answer:
Basic proportionality theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
As DE∥BC
∠ADE=∠ABC
∠AED=∠ACB
So by AAA property,
△ADE∼△ABC
Hence AB/AD =AC/AE
Since it is given that AC/AE =1/4
We get,AD/6 = 1/4
AD=1.5cm
So, AD=1.5cm
Given : In the triangle ABC , through the midpoint D of AB, A line segment DE parallel to BC is drawn, which intersects the side AC at the
point E
To Find : Ratio of AE/ AC
Solution:
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
DE || BC
=> AD/ DB = AE / EC
D is the mid point of AB
=> AD = DB = AB/2
=> AD/DB = 1
=> 1 = AE/ EC
EC = AC - AE
=> 1 = AE/( AC - AE)
=> AC - AE = AE
=> 2AE = AC
=> AE = AC/2
=> AE = (1/2) AC
correct answer is AE = (1/2) AC
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