Download Geometry Ch. 2 Review Lesson 2-1 Use Inductive Reasoning

Geometry Ch. 2 Review
Lesson 2-1
Use Inductive Reasoning – patterns
2, 6, 1, 7, 0, 8, -1, 9, -2, 10, -3, ___, ___, ____
True or False? If false, find a counterexample – Find something else to change the conclusion.
T/F If I like animals, I like pandas.
Counterex:
T/F If you are tall, you play basketball.
T/F If you like fruits, you like apples.
T/F If the figure has 4 sides, then it is a rectangle.
T/F If a figure has 4 congruent sides and 4 congruent angles, then it is a square.
Lesson 2-2
Conditional Statement
Converse
Inverse
Contrapositive
If p, then q.
If q, then p.
If not p, then not q.
If not q, then not p.
q (conclusion)
If p, then q.
Hypothesis – after “if” = p
Conclusion – after “then” = q
Lesson 2-3
Biconditional statements – p if and only if q
;
iff ;
p  q
True Biconditional – Conditional p q AND Converse qp are BOTH true.
Lesson 2-4 Algebra Proofs - Remember your properties!
Addition Property of Equality (=)
Subtraction Property of =
Multiplication Property of =
Division Property of =
Substitution Property
Distributive Property
Reflexive Property of =
Symmetric Property of =
Transitive Property of =
Reflexive Property of ≅
Symmetric Property of ≅
Transitive Property of ≅
Lesson 2-5 Vertical Angles
Vertical Angles are congruent
Part = Part
100
100
Linear Pair of Angles are supplementary (adds to 180)
Part + Part = 180
100
80
P (hypothesis)
Lesson 2-6 Geometry Proofs
Know some properties (plus more!)
Vertical Angles Theorem
Definition of Congruence
Reflexive, Symmetric, Transitive Property of = / ≅
Definition of right angle
Definition of supplementary angles
Definition of complementary angles
Segment Addition Postulate
Angle Addition Postulate
------------------------------------------------------------------------------------------------------------------------------Logic (Honors Geo only)
1) Conditional (If, then):
p
q
p q
T
T
T
T
F
F
F
T
T
F
F
T
2) Conjunction (AND)
p
q
p^q
T
T
T
T
F
F
F
T
F
F
F
F
3) Disjunction (OR)
p
q
T
T
T
F
F
T
F
F
pvq
T
T
T
F
Know how to solve QUADRATIC EQUATIONS (Honors Geo Only)
SET all = 0 and FACTOR
2
2
x – 7x = 8  x – 7x – 8 = 0  (x + 1) (x – 8) = 0  x = -1 & x = 8
x2 = 2x – 24  x2 – 2x +24 = 0  (x + 4) (x – 6) = 0  x = -4 & x = 6
Know how to solve equations with TWO variables (Honors Geo Only)
System of Equations
By Substitution
By Elimination
Helpful Properties and Theorems to help with PROOFS!
Statements
Reasons
1) m  1 = m  3
1) Given
2) m  1 + m  2 = m  3 + m  2
2) Addition prop. of =
Statements
Reasons
1) m  1 + m  2 = m  3 + m  2
1) Given
2) m  1 = m  3
2) Subtraction prop. of =
W
Statements
Reasons
1) m  WOY = m  1 + m  2
1) Angle Addition Postulate
Statements
Reasons
1) LH = LA + AH
1) Segment Addition Postulate
Statements
Reasons
2) ∠1 ≅ ∠3
2) Vertical Angles Theorem
(Vertical Angles are Congruent)
Statements
Reasons
1) AH = AH
1) Reflexive prop. of =
Statements
Reasons
1) 33 = x
1) Given
2) x = 33
2) Symmetric prop. of =
Statements
Reasons
1) ∠1 ≅ ∠2
1) Given
2) ∠1 ≅ ∠3
2) Vertical Angles Theorem
3) ∠2 ≅ ∠3
3) Transitive prop. of ≅
Y
X
1 2
O
L
●
H
●
A
●
2
1
3
●
1
●
3
Statements
Reasons
●I
1) FR bisects IFG
1) Given
R●
2) ∠IRF ≅ ∠GRF
2) Def of Angle Bisector
Statements
Reasons
1) A is the midpoint of ̅̅̅̅
𝐿𝐻
1) Given
2) ̅̅̅̅
𝐿𝐴 ≅ ̅̅̅̅
𝐻𝐴
2) Def of Midpoint
Statements
Reasons
1) ∠1 & ∠2 are
complementary angles.
2) 𝑚∠1 + 𝑚∠2 = 90
1) Given
Statements
Reasons
1) ∠1 & ∠2 are
supplementary angles.
2) 𝑚∠1 + 𝑚∠2 = 180
1) Given
Statements
Reasons
1) ∠1 is a right angle.
1) Given
2) 𝑚∠1 = 90
2) Def of Right Angle
Statements
Reasons
1) m2  m3
1) Given
2) 2  3
2) Def of Congruence
Statements
Reasons
1) 2  3
1) Given
2) m2  m3
2) Def of Congruence
F
●
●
G
A
●
L
●
H
●
1 2
2) Def of Complementary Angles
2
●
1
2) Def of Supplementary Angles
1
PRACTICE - Your Turn! Fill in the blank
Statements
Reasons
1) m  1 = m  3
1) Given
2) m  1 + m  2 = m  3 + m  2
2)
Statements
Reasons
1) m  1 + m  2 = m  3 + m  2
1) Given
2) m  1 = m  3
2)
Name: _________________________
W
Statements
Reasons
1) m  WOY = m  1 + m  2
1)
Statements
Reasons
1) LH = LA + AH
1)
Statements
Reasons
2) ∠1 ≅ ∠3
2)
1 2
O
L
●
H
●
A
●
Reasons
1) AH = AH
1)
Statements
Reasons
1) 33 = x
1) Given
2) x = 33
2)
Statements
Reasons
1) ∠1 ≅ ∠2
1) Given
2
1
3
●
1
Statements
Y
X
●
3
2) ∠1 ≅ ∠3
2) Vertical Angles Theorem
3) ∠2 ≅ ∠3
3)
Statements
Reasons
●I
1) FR bisects IFG
1) Given
R●
2) ∠IRF ≅ ∠GRF
2)
Statements
Reasons
̅̅̅̅
1) A is the midpoint of 𝐿𝐻
1) Given
̅̅̅̅ ≅ 𝐻𝐴
̅̅̅̅
2) 𝐿𝐴
2)
Statements
Reasons
1) ∠1 & ∠2 are
complementary angles.
2) 𝑚∠1 + 𝑚∠2 = 90
1) Given
Statements
Reasons
1) ∠1 & ∠2 are
supplementary angles.
2) 𝑚∠1 + 𝑚∠2 = 180
1) Given
Statements
Reasons
1) ∠1 is a right angle.
1) Given
2) 𝑚∠1 = 90
2)
Statements
Reasons
1) m2  m3
1) Given
2) 2  3
2)
Statements
Reasons
F
●
●
G
A
●
L
●
H
●
1 2
2)
2
●
1
2)
1
1) 2  3
1) Given
2) m2  m3
2)