Chapter 2, lesson 4: Axioms and equals SWBAT: Identify axioms used to solve algebraic equation Use axioms to solve geometric problems

Axiom 1 Things that are equal to the same thing are equal to each other. If a = b and b = c, then a = c. Axiom 2 If equals are added to equals, the sums are equal. If a = b and c = d, then a + c = b + d. Axiom 3 If equals are subtracted from equals, the differences are equal. If a = b and c = d, then a – c = b – d. Axiom 4 Things that are alike or coincide with one another are equal to one another. Example : Segment AB = Segment BA ; ∠A = ∠A  Axiom 5 The whole, or sum, is greater than the parts. A + B = C A and B > 0 then C > A and C > B

Axiom 4 Things that are alike or coincide with one another are equal to one another. On its face, Axiom 4 seems to say that a thing is equal to itself, but it looks like Euclid also used it justify the use of a technique called superposition to prove that things are congruent. Basically, superposition says that if two objects (angles, line segments, polygons, etc.) can be lined up so that all their corresponding parts are exactly on top of each other, then the objects are congruent.

Read pages 51–52. Complete Workbook 15-17

A postulate is a statement that is assumed true without proof A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. 

Vertical angles are a pair of non-adjacent angles formed when two lines intersect.