Question

state Thales theorem​

Answer 1

Answer:

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements.

Answer 2

Answer:

Basic Proportionality theorem was introduced by a famous Greek Mathematician, Thales, hence it is also called Thales Theorem.

Step-by-step explanation:

Basic Proportionality Theorem Proof↴

Let us now try to prove the basic proportionality theorem statement

Consider a triangle ΔABC, as shown in the given figure. In this triangle, we draw a line PQ parallel to the side BC of ΔABC and intersecting the sides AB and AC in P and Q, respectively.

According to the basic proportionality theorem as stated above, we need to prove:

AP/PB = AQ/QC

Solved Example↴

✎ In a ∆ABC, sides AB and AC are intersected by a line at D and E respectively, which is parallel to side BC. Then prove that AD/AB = AE/AC.

Solution: 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.

${}$