1 / 12

Axioms

Common Notions. Axioms. Students will be able to identify the axioms used to solve algebraic equations Students will be able to solve geometric problems Axioms: a statement assumed to be true without proof. Objectives. Things that are equal to the same thing are equal to each other.

zandra
Download Presentation

Axioms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Common Notions Axioms

  2. Students will be able to identify the axioms used to solve algebraic equations Students will be able to solve geometric problems Axioms: a statement assumed to be true without proof. Objectives

  3. Things that are equal to the same thing are equal to each other. • In Algebraic terms: • If a = b • b = c • Then a = c • You might think of this as substituting c for b Axiom 1

  4. If equals are added to equals, the sums are equal. • In Algebra Terms: • If a = b and c = d • Then a + c = b + d Axiom 2

  5. If equals are subtracted from equals, the differences are equal. • In Algebra Terms: • If a = b and c = d • Then a - c = b - d Axiom 3

  6. Things that are alike or coincide with each other are equal to one another. • In Algebra Terms: • Two figures that can be made to match each other, point for point are equal. Axiom 4

  7. The whole, or sum, is greater than the parts. • In Algebra Terms: • If a + b = c • a & b > 0 • Then c > a & c > b Axiom 5

  8. Given: x – 3 = 10 +3 +3 x = 13 • Reason: • Axiom 2: If equals are added to equals, then the sums are equal. Example 1

  9. Given: x + 3 = 10 -3 -3 x = 7 • Reason: • Axiom 3: If equals are subtracted from equals, then the differences are equal. Example 2

  10. Given: 1 yard = 3 feet 1 foot = 12 inches 1 yard = 3(12 inches) = 36 inches • Reason: • Axiom 1: Things that are equal to the same thing are equal to each other. Example 3

  11. Given: The upper half circle, called a semicircle, completely matches the lower half. (Think of folding the together along the center line or diameter.) • Therefore, the semicircles are equal. • Reason: • Axiom 4: Things that are alike or coincide with each other are equal to one another. Example 4

  12. Given: m ABD + m DBC = 180o • Therefore: 180o > ABD and 180o > DBC • Reason: • Axiom 5: The whole, or sum, is greater than the parts. Example 5

More Related