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## What is Thales theorem explain with proof?

In geometry, Thales’ 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.

**Is Thales theorem and basic proportionality theorem same?**

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).

**What is the main philosophy of Thales?**

Thales was the founder of the philosophy that all of Nature had developed from one source. According to Heraclitus Homericus (540–480 BCE), Thales drew this conclusion from the observation that most things turn into air, slime, and earth. Thales thus proposed that things change from one form to another.

### How do you prove converse of the Thales theorem?

- Statement : If a line divide any two sides of a triangle (Δ) in the same ration, then the line must be parallel (||) to third side.
- Given in ΔABC, D and E are two points of AB and AC respectively, such that,
- Let us assume that in ΔABC, the point F is an intersect on the side AC.

**Which theorem is known as Thales theorem?**

basic proportionality theorem

The intercept theorem, also known as Thales’s theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.

**Which theorem is also known as Thales Theorem?**

## Which of following theorem is also known as Thales Theorem?

The basic proportionality theorem, also known as the Thales theorem states that “the line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion”.

**What is Thale’s theorem?**

Thale’s theorem is basically a special case of the inscribed angle theorem in Circular geometry : If there are three points A,B and C on the circumference of the circle such that A,B describe the diameter of the circle, then the angle ACB is a right angle. In other words, the diameter of a circle always subtends a right angle at its circumference.

**What is the converse of the right angle theorem?**

If a triangle is inscribed inside a circle, where one side of the triangle is the diameter of the circle, then the angle opposite to that side is a right angle. The converse of this is also true. There are many ways to prove this theorem.

### What is the intercept theorem for inscribed angles?

One is the Intercept Theorem for the ratios between the line segments created when two parallel lines are intercepted by two intersecting lines, and here we’ll prove another one, related to inscribed angles. The theorem states that any inscribed angle in a circle that subtends the diameter is a right angle.

**How do you prove a triangle has a right angle?**

Which states that any triangle raised on the diameter of a circle has a right angle. So, in other words, picture a circle. Cut it in half with a diameter. Now raise a triangle, using this diameter as one of its sides, and the third vertex of the triangle is on the circle somewhere.