Thales Theorem
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Thales or "Thales of Miletus"
Thales used geometry to solve problems such as calculating the height and length of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry by deriving the four corollaries of Thales Theorem. Also, thales contributed five theorems on the field of geometry. He was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regarding him as the first philosopher in the Greek tradition. Aristotle reported Thales' hypothesis about the nature of matter that the originating principle of nature was a single material substance that is water.
Thales used geometry to solve problems such as calculating the height and length of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry by deriving the four corollaries of Thales Theorem. Also, thales contributed five theorems on the field of geometry. He was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regarding him as the first philosopher in the Greek tradition. Aristotle reported Thales' hypothesis about the nature of matter that the originating principle of nature was a single material substance that is water.
Thales Five Theorems in Geometry
1. A circle is bisected by its diameter.
2. Angles at the base of any isosceles triangle are equal.
3. If two straight lines intersect, the opposite angles formed are equal. (Vertical Angle)
4. If one triangle has two angles and one side are equal to another triangle, the two triangles are equal
in all respects. (Side Angle Angle Congruence)
5. Any angle inscribe in a semi-circle is a right angle.
1. A circle is bisected by its diameter.
2. Angles at the base of any isosceles triangle are equal.
3. If two straight lines intersect, the opposite angles formed are equal. (Vertical Angle)
4. If one triangle has two angles and one side are equal to another triangle, the two triangles are equal
in all respects. (Side Angle Angle Congruence)
5. Any angle inscribe in a semi-circle is a right angle.
Thales Theorem In geometry, Thales' theorem states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem, and is mentioned and proved on the 33rd proposition, third book of Euclid's Elements. It is generally attributed toThales of Miletus, who is said to have offered an ox (probably to the god Apollo) as a sacrifice of thanksgiving for the discovery, but sometimes it is attributed to Pythagoras.
Inscribed Angle
In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.
Inscribe Angle Conditions:
a. Its vertex is on the arc but not the endpoints of the arc.
b. The sides of the angle contained the endpoints of the arc.
In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.
Inscribe Angle Conditions:
a. Its vertex is on the arc but not the endpoints of the arc.
b. The sides of the angle contained the endpoints of the arc.