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Some Properties.

(1) Reflexive Property-- A quantity is congruent (equal) to itself. \(a=a\)

(2) Symmetric Property-- If \(a = b\), then \(b = a\).

(3) Transitive Property-- If \(a = b\) and \(b = c\), then \(a = c\).

(4) Addition Postulate-- If equal quantities are added to equal quantities, the sums are equal.

(5) Subtraction Postulate-- If equal quantities are subtracted from equal quantities, the differences are equal.

(6) Multiplication Postulate-- If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.)

(7) Division Postulate-- If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.)

(8) Substitution Postulate-- A quantity may be substituted for its equal in any expression.

(9) Partition Postulate-- The whole is equal to the sum of its parts.

Also: Betweeness of Points: \(AB + BC = AC\).

Angle Addition Postulate: \(\angle ABC + \angle CBD = \angle ABD\).

(10) Construction-- Two points determine a straight line.

(11) Construction-- From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line.

Note by Sattik Biswas
6 months, 1 week ago

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This is interesting. Why don't you add a small introduction at the top?

As a moderator, I am very appreciative of your notes. Since you are into this, I suggest you read what other people share too for inspiration. You'll find some intriguing examples at the bottom of this page Agnishom Chattopadhyay · 5 months, 3 weeks ago

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@Agnishom Chattopadhyay Also, you could contribute your knowledge in the wikis

Several of them need examples, feedback and completion. You could also start your own wiki. You could let the world know about them by maintaining a note like this or sharing the wiki links on social media Agnishom Chattopadhyay · 5 months, 3 weeks ago

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@Agnishom Chattopadhyay Okay thanks! Sattik Biswas · 5 months, 3 weeks ago

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You are really diverse, i must say. From reflexive and symmetric to primitive roots. Wow! Rakhi Bhattacharyya · 5 months, 3 weeks ago

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@Rakhi Bhattacharyya hahaha yup I am.. Sattik Biswas · 5 months, 3 weeks ago

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@Sattik Biswas I just like to explore the world. Sattik Biswas · 5 months, 3 weeks ago

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