Question

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о Prove Thale's Theorem.
о Proper Explanation needed.
о No spams.

Answer 1

Step-by-step explanation:

Given,

DE || BC

So, AD/DB = AE/EC

or we can interchange the ratios as;

DB/AD = EC/AE

Now, add 1 on both sides;

(DB/AD) + 1 = (EC/AE) + 1

(DB + AD)/AD = (EC + AE)/AE

AB/AD = AC/ AE

If we interchange the ratios again, we get;

AD/AB = AE/AC

Hence, proved.

2. Suppose a triangle ABC, where DE is a line drawn from the midpoint of AB and ends midpoint of AC at E. AD/DB = AE/EC and ∠ADE = ∠ACB. Then prove ABC is an isosceles triangle.

Solution: Given,

AD/DB = AE/EC

By the converse of basic proportionality theorem, we get;

DE || BC

But it is given that,

∠ADE = ∠ACB

Hence,

∠ABC = ∠ACB

The side opposite to equal angles is also equal.

AB = AC

Hence, ABC is an isosceles triangle.