Question

In fig D is the mid point of A B and DE||BC . Then AE is equal to-
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Answer 1

Answer:

AE=AC

Step-by-step explanation:

Answer 2

Given,

In a ∆ABC;

AD = DB

DE || BC

To find,

The equivalent of AE.

Solution,

We can simply solve this mathematical problem using the following process:

Geometrically,

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

(Triangle proportionality theorem)

Now, according to the question;

AD = DB

=> AD:DB = 1:1

AD:DB = 1:1{Equation-1}

Now, according to the question;

In the given ∆ABC,

In the given ∆ABC,DE is a line parallel to BC side of a triangle and it intersects the other two sides of the triangle. Then, according to the triangle proportionality theorem, the line DE divides these the sides AB and AC proportionally.

=> AD:DB = AE:EC

=> AE:EC = 1:1 (according to the equation-1)

=> AE = EC

=> EC is equivalent to AE

Hence, AE is equal to EC.