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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 ...

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 ...

### Intro to the Pythagorean theorem (video) | Khan Academy

Sal introduces the famous and super important Pythagorean theorem! ... Practice:
Use Pythagorean theorem to find right triangle side lengths · Use Pythagorean
theorem to find area of an ..... In the case of 5, 12 and 13 : 5^2 + 12^2 = 25 + 144
= 169 = 13^2. Comment .... Yes, square root is the inverse of a square. Comment.

### Circle Geometry

https://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 ...

### 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.

### 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 ...

### Arcs and Chords

https://www.cliffsnotes.com/study-guides/.../circles/arcs-and-chords

Theorem 78: In a circle, if two chords are equal in measure, then their
corresponding minor arcs are equal in measure. The converse of this theorem is
also true. ... Figure 3 A diameter that is perpendicular to a chord. ... OA = 13 and
AM = 5, OM can be found by using the Pythagorean Theorem. ... triple. In either
case, OM = 3.

### 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.

### Solving Problems Involving the Pythagorean Theorem

www.mesacc.edu/~scotz47781/mat120/notes/.../pythag_thm.html

Step 2: Use the Pythagorean Theorem (a2 + b2 = c2) to write an equation to be
solved. ... In the case, we need to get the equation equal to zero and solve by
factoring. Step 4. Step 5: ... Example 3 – A guy wire is attached to a telephone
pole.

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