Powerpoint Project 5 Adam and Nikki Birnbrey
Properties of Equality to Know and Love Addition Property- If a=b, then a+c= b+c Subtraction Property- If a=b, then a-c=b-c Multiplication Property- If a=b, then ac=bc Division Property- If a=b and c doesn’t = 0 Then a/c= b/c Substitution Property- If a=b you may replace a with b in any equation containing a in the result
Equivalence Properties of Equality to Know and Love Reflexive Property- For any real number a, a=a Symmetric Property- For all real numbers a and b, if a=b, then b=a Transitive Property- For all real numbers a, b, and c, if a=b and b=c, then a=c
Equivalence Relation To Know And Love = any relation that satisfies these equivalence properties Reflexive Property- Figure A=Figure A A Symmetric Property- If Figure A=Figure B, then Figure B=Figure A A Transitive Property- If Figure A=Figure B and Figure B=Figure C, Then Figure A=Figure C A B C
Overlapping Theorem to Know and Love Overlapping Segments- Given a segment with points A, B, C, & D arranged as shown the following statements are true: 1. If AB=CD then AC=BD 2. If AC=BD then AB=CD Overlapping Angles- Given Angle AED with points B and C in its interior as shown, the following statements are true: 1. If Angle AEB=Angle CED then ? 2. If Angle AEC=Angle BED then ? A B C D AB E C D
Vertical Angles Theorem to Know and Love IIf two angles form a pair of vertical angles, then they are congruent. Given: angle 1 and 2 are vertical angles Prove: Angle 1 and 2 are congruent Statements Reasons 1.Angle 1 and 2 are vertical angles 2. Angle 1 + angle 2= 180 Angle 2 + angle 3= Angle 1+ angle 3= angle 2 + angle 3 4.Angle 1= angle 2 (1=2) Given Linear pair property Substitution property of equality Subtraction property of equality
Congruence Supplements Theorem to Know and Love If two angles are supplements of congruent angles then the two angles are congruent Given: Angle 1=Angle 3, Angle 1 and angle 2 are supplementary, Angle 3 and 4 are supplementary Prove: Angle 2=Angle 4 Statements Reasons 1. <1+<2=180 <3+<4= <1+<2=<3+<4 3. <1=<3 4. <1+<2=<1+<4 5. <2=<4 Definition of Supplementary Angles Transitive Given Substitution Property Subtraction Property 3412
More Theorems to Know and Love Theorem- Reflection across two parallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines Theorem- Reflection across two intersecting lines is equivalent to a rotation about the point of intersection through twice the measure of the angle between the lines
Vocabulary to Know and Love Equivalence relation= Any relation that satisfies the Reflexive, Symmetric, and Transitive Properties Inductive reasoning= The process of forming conjectures that are based on observations Paragraph proof= A form of a proof in which one’s reasoning is explained in paragraph form, as opposed to a two-column proof Theorem= A statement that has been proved deductively Two column proof= A proof in which the statements are written in the left-hand column and the reasons are given in the right-hand column Vertical angles= The opposite angles formed by two intersecting lines
Practice to Know and Love (and a pooton of it) VVertical Angles: Definition, illustrated examples, and an interactive practice quiz
A real pooton of Practice to Know and Love (yeah math ) Given: 15x-5=10x+15 (use properties to prove) Prove the Overlapping Segments Theorem Given: WX=YZ; Prove WY=XZ W XY Z WX=YZ WX+XY= YZ+XY WX=XY=WY segment additon postulate ______property
….Extra poo Identify the properties of equality that justify the conclusion. <B= <C; <C= <D <B= <D ________ AB=CD; CD=AB_______ AB+BC= BC+ CD; AC=BD_______
Finding Values: Problemas (To Know and Love) Find x. 3X- 60 X X 10X