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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.
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