PROVING STATEMENTS IN GEOMETRY

WHAT IS A PROOF? A written account of the complete thought process that is used to reach a conclusion. Each step is supported by a theorem, postulate or definition

WHAT IS IN A PROOF? A statement of the original problem A diagram, marked with “Given” information Re-statement of the “Given” information Complete supporting reasons for each step The “prove” statement as the last statement –Sometimes Q.E.D. is written “quod erat demonstrandum” Latin for “which was to be demonstrated”

THE TWO COLUMN PROOF STATEMENT REASON On this side –Definitions –Postulates –Theorems –Properties of shapes

YOU KNOW WHAT THEY SAY ABOUT ASSUMING… Yes, you look at pictures. Yes, things will probably be drawn so that they look accurate. However, unless there are marks or written givens, you cannot assume: –Angles or segments are congruent –An angle is a right angle –Lines are parallel –Lines are perpendicular

WITHOUT MARKS ON OUR DIAGRAM OR WRITTEN WORD… We CANNOT assume... Lines a and b are parallel We CANNOT assume... Triangle ABC is a right triangle

PROPERTIES Reflexive property: A segment or angles is congruent to itself.

Transitive property: If two or more segments or angles are congruent to the same segment or angle, then they are congruent to each other.

Symmetric property: A congruence can be stated in either order (congruence is commutative)

PRACTICE Name the property that is being used in the following statements… Transitive Reflexive Symmetric