2-1/2-2
p: if you are a guitar player q: you are a musician
Write each statement in the correct form and decide if it is true or false
p-->q
If you are a guitar player, then you are a musician.
True
9+16=16+9
7+(1-6)=(7+1)-6
11(2x+3)=22x+33
Commutative Property
Associative Property
Distributive Property
What is the definition of Given?
Something in a problem you may assume is true.
What property was used here?
6x = 2x-8
4x=8
Subtraction property of equality
If two angles are complementary then they are congruent. What theorem is this?
Congruent Complements Theorem
p: if you are a guitar player q: you are a musician
Write each statement in the correct form and decide if it is true or false
~q-->~p
If you are not a musician, then you aren't a guitar player
True
3x-2=17, so 3x=19
2x=66, so x=33
If XY=3x+7 and x=9, then XY= 3(9)+7
Addition Property of Equality
Division Property of Equality
Substitution Property
Create a proof for the equation x-3=0, proving that x=3.
Show Whiteboard
If a point separates a line segment into two equal parts, what is it called?
A midpoint
What is a flowchart proof?
A chart showing the logical flow of a proof using boxes and arrows.
p: if you are a guitar player q: you are a musician
Write each statement in the correct form and decide if it is true or false
~p-->~q
False
6=6
2(x)=(x)2
If AB=19 and CD=19, then AB=CD
Reflexive Property
Symmetric Property
Transitive Property
What is a list of justifications for each step you take in solving a problem?
A proof
If a line or ray separates an angle into two equal smaller angles, what is it called?
An angle bisector
What property is when you can add or subtract the same value from both sides of the equation and it remains equal?
Addition Property of Equality
Inductive or Deductive
Every student that studies does well. Samantha studies so she did well.
Inductive
If m∠UVW= m∠QRS, then ∠UVW ≅∠QRS
ST+TU=SU
∠B and ∠E are right angles, therefore ∠B≅∠E
Definition of Congruence
Segment Addition Postulate
All Right Angles are Congruent
Create a proof for the equation 5x=25, proving that x=5.
Show Whiteboard.
What is the name of the postulate or theorem of adding two adjacent angles?
Angle addition postulate
How are paragraph proofs different than regular proofs?
They made with questions like a narrative.
Inductive or Deductive?
Jim has 20 pencils. He gives 1/2 of them to Dan. Jim now has 10 pencils.
Deductive
If AB ⟂ CD, then ∠CEB, ∠BED are right angles. So ∠CEB = 90°, ∠BED = 90°
M is the midpoint of AB, therefore AM=MB
∠ABD +∠CBD=∠ABC
Definition of Perpendicular
Definition of Midpoint
Angle Addition Postulate
Create a proof for the equation 3x+14=23, proving that x=3.
Show whiteboard.
Prove the Vertical Angles Theorem up on the white board
m<1+m<2=180 -- linear pair theorem
m<2+m<3=180 -- linear pair theorem
m<1+m<2=m<2+m<3 -- transitive property
m<1=m<3 -- subtraction property of equality
<1≅<3 -- definition of congruence
What do the arrows show?
Direction of the steps/logic