Question

◆ Prove Thale's Theorem.
◆ No spams ​

Answer 1

Answer:

Thales theorem is a special case of the inscribed angle theorem (the central angle = twice the inscribed angle).

Thales theorem is attributed to Thales, a Greek mathematician and philosopher who was based in Miletus. Thales first initiated and formulated the Theoretical Study of Geometry to make astronomy a more exact science.

There are multiple ways to prove Thales Theorem.

We can use geometry and algebra techniques to prove this theorem. Since this is a geometry topic, therefore, let’s see the most basic method below.

How to Solve the Thales Theorem?

• To prove the Thales theorem, draw a perpendicular bisector of ∠
• Let point M be the midpoint point of line AC.
• Also let ∠MBA = ∠BAM = β and ∠MBC =∠BCM =α
• Line AM = MB = MC = the radius of the circle.
• ΔAMB and ΔMCB are isosceles triangles.

Applications of Thales

Theorem In geometry, none of the topics are without any real-life use. Therefore, Thales Theorem also has some applications:

• We can accurately draw a tangent to a circle using Thales Theorem. You can use a set square for this purpose.
• We can accurately find the center of the circle using the Thales Theorem. The tools used for this application are a set square and a sheet of paper. Firstly, you have to place the angle at the circumference—the intersections of two points with circumference state the diameter. You can repeat this using different pair of points, which will give you another diameter. The intersection of diameters will give you the center of the circle.

Answer 2

To prove the Thales theorem, draw a perpendicular bisector of ∠

Let point M be the midpoint point of line AC.

Also let ∠MBA = ∠BAM = β and ∠MBC =∠BCM =α

Line AM = MB = MC = the radius of the circle.

ΔAMB and ΔMCB are isosceles triangles.

According to BPT theorem, for any two equiangular triangles, the ratio of any two corresponding sides is always the same.

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