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Pythagorean triple - Wikipedia

https://en.wikipedia.org/wiki/Pythagorean_triple

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 +
b2 = c2. ... 3.1 General properties; 3.2 Special cases .... Many formulas for
generating triples with particular properties have been developed since the time
of Euclid. ..... As for any right triangle, the converse of Thales' theorem says that
the ...

The Pythagorean Theorem: Converse and Special Cases Video with ...

https://study.com/.../the-pythagorean-theorem-converse-and-special-cases. html

The Pythagorean Theorem is a famous theorem for right triangles. Watch this
video to learn how the Pythagorean Theorem relates to the law of cosines and
how ...

Circle Geometry

www.amsi.org.au/teacher_modules/Circle_Geometry.html

b: Which of the transformations in part a map a particular point P on script_l to
another .... Two practical situations to illustrate the converse theorem. A set of
points ..... The following theorem makes the situation clear, and uses Pythagoras'
theorem in its proof. .... i are one inside the other, ii touch internally, iii overlap, iv
touch ...

Special right triangles proof (part 1) (video) | Khan Academy

Since we all have squares because of the Pythagorean theorem (a²+b²=c²), ...
Since at least in this case, the hypotenuse is x and the smaller side opposite to
the ...

Mathematical Statements

discrete.openmathbooks.org/dmoi3/sec_intro-statements.html

This could be done by specifying a specific substitution, for example, “3+x=12 3 +
x = 12 where x=9, x = 9 .... Consider the Pythagorean Theorem. ... Did I lie in
either case? .... However, sometimes the converse of a true statement is also true.

Pythagorean theorem proof using similarity (video) | Khan Academy

Proof of the Pythagorean Theorem using similarity. ... The Pythagorean Theorem
is just a special case of another deeper theorem from Trigonometry called the ...

Geometry

https://www.doe.in.gov/.../contentconnector-20180721-math-geometry.pdf

Jul 21, 2018 ... try special cases and simpler forms of the original problem in order to gain insight
into its solution .... G.PL.3.a.1: Identify angle relationships when a ... conversely;
the Pythagorean Theorem, using triangle similarity ... converse.

Pythagorean theorem example (video) | Khan Academy

Sal uses the Pythagorean theorem to find the height of a right triangle with a base
of ... As I said before, the Pythagorean Theorem is a special case of the Law of ...

Right Triangles

https://www2.clarku.edu/faculty/djoyce/trig/right.html

We can use the Pythagorean theorem and properties of sines, cosines, and ...
Let's first look at some cases where we don't know all the sides. ... On a calculator
, we use the inverse trig functions named arctangent, arcsine, and arccosine. .... (
ii) in terms of the apothem r, that is, the radius of the inscribed circle, and (iii) in ...

Pythagorean Theorem and its many proofs

https://www.cut-the-knot.org/pythagoras/

122 proofs of the Pythagorean theorem: squares on the legs of a right triangle
add up ... The converse states that a triangle whose sides satisfy a² + b² = c² is ....
that the configuration exploited in this proof is just a specific case of the one from
the ...... Tony Foster, III, submitted a number of proofs that made use of a property
of ...

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