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Theorem of Thales

Thales Melet (around 624 to 548 B.C.) was the first Greek mathematician - do my homework - of antiquity to make general statements about mathematical objects and to give logical reasons for them. Along with his student Pythagoras, he was one of the pioneers of a new stage in the development of mathematics.

When he discovered during a stay in Egypt that a circle can always be drawn around a right-angled triangle - math homework solver , he sacrificed an ox for this discovery.

Theorem of Thales

Every circumferential angle above a semicircle (or above the diameter of a circle) is a right angle.

Proof (with the help of the sum of angles in isosceles triangles).

Prerequisite:

A, B and C lie on the circle around M.

AB is the diameter of the circle.

Assertion:

γ=90°

Proof:

It holds: α=γ1 and β=γ2 (base angles in the isosceles triangles AMC and MBC).

It follows: α+β=γ1+γ2=γ

Since α+β+γ=180° (sum of angles in triangle) also holds , 2⋅γ=180° or γ=90°. (w. b. w.)

Proof (using the mirror image of triangle ABC)

The triangle ABC is mirrored at AB. The image of C is the point D. The quadrilateral ADBC is a chordal quadrilateral - https://domyhomework.club/geometry-homework/ . Therefore the angles in D and in C complement each other to 180°. Because the angle in D is the image of the angle in C when mirrored at AB, both angles are congruent to each other and therefore right angles.