Question

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last question :-
state and prove BPT (Thales theorem).

Miss Izzatdar ♡~​

Answer 1

Answer:

Basic Proportionality theorem was introduced by a famous Greek Mathematician, Thales, hence it is also called Thales Theorem. According to him, for any two equiangular triangles, the ratio of any two corresponding sides is always the same. Based on this concept, he gave theorem of basic proportionality (BPT). This concept has been introduced in similar triangles. If two triangles are similar to each other then,

i) Corresponding angles of both the triangles are equal

ii) Corresponding sides of both the triangles are in proportion to each other

Proof

Suppose a line DE, intersects the two sides of a triangle AB and AC at D and E, such that;

AD/DB = AE/EC ……(1)

Assume DE is not parallel to BC. Now, draw a line DE’ parallel to BC.

Hence, by similar triangles,

AD/DB = AE’/E’C ……(2)

From eq. 1 and 2, we get;

AE/EC = AE’/E’C

Adding 1 on both the sides;

AE/EC + 1 = AE’/E’C +1

(AE +EC)/EC = (AE’+E’C)/E’C

AC/EC = AC/E’C

So, EC = E’C

This is possible only when E and E’ coincide.

But, DE’ || BC

Therefore, DE ||BC.

Hence, proved.

Answer 2

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State and prove Basic Proportionality theorem.

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