Detailed Chapter on Thales Theorem

In this article, we’ll learn more about the hypotenuse leg (HL) theorem. Like, SAS, SSS, ASA, and AAS, it is also one of the congruencies proposes of a triangle. Let’s learn more about Thales theorem.

The distinction is that the other four proposes apply to all triangles. Simultaneously, the Hypotenuse Leg Theory holds for the ideal triangles just because hypotenuse is one of the legs of right-angled triangular.

What is Hypotenuse Leg Theorem or Thales Theorem?

The hypotenuse leg theorem is a criterion used to confirm whether a provided set of right triangular is consistent.

The hypotenuse leg (HL) theory states that; an offered triangular set is congruent if the matching sizes of their hypotenuse and one leg are equivalent.

Unlike various other congruency proposes such as; SSS, SAS, ASA, and AAS, three quantities are examined, with hypotenuse leg (HL) theory, two sides of an appropriate triangular are only thought about.

Rational Expressions – Partial Portion Decomposition



Proof of Hypotenuse Leg Theorem

If the representation over, triangles ABC and PQR are right triangles with Abdominal Muscle = RQ, A/C = PQ.

By Pythagorean Theory,

AC2 = AB2 + BC2 as well as PQ2 = RQ2 + RP2

Because, Air Conditioning = PQ, an alternative to obtaining;

AB2 + BC2 = RQ2 + RP2

However, AB = RQ,

By substitution;

RQ2 + BC2 = RQ2 + RP2

Gather like terms to obtain;

BC2 =RP2.

For this reason, △ ABC ≅ △ PQR.

More details about Thales Theorem

Put another way: If a triangular has, as one side, the diameter of a circle, and also the 3rd vertex of the triangular is any point on the area of the circle, after that the triangle will certainly always be an appropriate triangular.

In the number above, despite how you move the factors P, Q, and R, the triangle PQR is always right triangular. The angle ∠ PRQ is continuously appropriate.

The reverse of Thales Theory works when you are searching for the facility of a circle. In the figure over, an ideal angle whose vertex is always “cuts off” the circle’s diameter. That is, the factors P and Q are still the ends of a size line.

Given that the diameter goes through the center, by drawing two such diameters, the center is located at the point where the diameters intersect.

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