2.1 Conditional Statements Day 1 Part 1 CA Standards 1.0, 3.0Slide 2
Warmup State whether each sentence is valid or false. On the off chance that you live in Los Angeles, then you live in California. In the event that you live in California, then you live in Los Angeles. In the event that today is Wednesday, then tomorrow is Thursday. On the off chance that tomorrow is Thursday, then today is Wednesday. Genuine False TrueSlide 3
Conditional Statement Conditional explanation has two sections, speculation and a conclusion. On the off chance that _____________, then____________. speculation conclusionSlide 4
Rewrite in If-Then shape A number separable by 9 is additionally distinct by 3. In the event that a number is detachable by 9, then it is distinguishable by 3. Two focuses are collinear on the off chance that they lie on a similar line. In the event that two focuses lie on a similar line, then they are collinear.Slide 5
Writing a Counterexample Write a counterexample to demonstrate that the accompanying restrictive explanation is false. On the off chance that x 2 = 16, then x = 4.Slide 6
Converse Two focuses are collinear in the event that they lie on a similar line. On the off chance that two focuses are collinear, then they lie on a similar line. In the event that two focuses lie on a similar line, then they are collinear. Contingent Statement ConverseSlide 7
An announcement can be changed by nullification , that is, by composing the negative of the announcement. Articulation: m<A = 30° Negation: m < A ≠ 30° Statement: <A is intense. Invalidation: <A is not intense.Slide 8
Inverse If two focuses lie on a similar line, then they are collinear. In the event that two focuses don\'t lie on a similar line, then they are not collinear. Restrictive InverseSlide 9
Contrapositive If two focuses lie on a similar line, then they are collinear. In the event that two focuses are not collinear, then they don\'t lie on a similar line. Contingent ContrapositiveSlide 10
When two articulations are both valid or both false, they are called comparable proclamations. A contingent proclamation is proportional to its contrapositive. The opposite and opposite of any restrictive proclamation are proportional.Slide 11
Write the a) reverse b) banter c) contrapositive If there is snow on the ground, then blossoms are not in sprout. In the event that there is no snow on the ground, then blossoms are in sprout. On the off chance that blossoms are not in sprout, then there is snow on the ground. In the event that blossoms are in sprout, then there is no snow on the ground.Slide 12
Point, Line, and Plane Postulates Postulate 5 Through any two focuses there exists precisely one line. Propose 6 A line contains no less than two focuses. Hypothesize 7 If two lines converge, then their convergence is precisely one point.Slide 13
Postulate 8 Through any three noncollinear focuses there exists precisely one plane. Propose 9 A plane contains no less than three noncollinear focuses. Hypothesize 10 If two focuses lie in a plane, then the line containing them lies in the plane.Slide 14
Postulate 11 If two planes converge, then their crossing point is a line.Slide 15
Review Write the opposite of the contingent proclamation. On the off chance that x = 3, then y = 7. On the off chance that Carrie joins the softball group, then Mary will join. In the event that two heavenly attendants are vertical, then their measures are equivalent.Slide 16
2.2 Definitions and Biconditional Statements Day 1 Part 2 CA Standards 1.0, 3.0Slide 17
Definition Two lines are called opposite lines on the off chance that they cross to frame a correct edge. A line opposite to a plane is a line that crosses the plane in an indicate and is opposite each line in the plane that converges it.Slide 18
Exercise Decide whether every announcement about the chart is valid. Clarify your answer utilizing the definitions you have learned. Focuses D, X, and B are collinear. Air conditioning is opposite to DB. <AXB is neighboring <CXD. . A . . D X B . CSlide 19
Biconditional Statement Biconditional Statement It is Saturday, just in the event that I am working at the eatery. Contingent Statement If it is Saturday, then I am working at the eatery.Slide 20
Consider the accompanying explanation x = 3 if and just if x 2 = 9. Is this a biconditional explanation? Yes Is the announcement genuine? No, in light of the fact that x likewise can be - 3.Slide 21
Rewrite the biconditional as restrictive proclamation and its opposite. Two edges are supplementary if and just if the entirety of their measures is 180°. Restrictive: If two edges are supplementary, then the aggregate of their measures is 180°. Speak: If the whole of two points measure 180°, then they are supplementary.Slide 22
State a counterexample that shows that the opposite of the announcement is false. On the off chance that three focuses are collinear, then they are coplanar. On the off chance that a point measures 48°, then it is intense.Slide 23
Pg. 75 # 4 – 38 even Handout 2.2Slide 24
2.3 Deductive Reasoning Day 2 Part 1 CA Standards 1.0, 3.0Slide 25
Warmup Rewrite the genuine proclamation in if-then frame and compose the opposite. In the event that the opposite is valid, join it with the if-then explanation to shape a genuine biconditional proclamation. The edge of a triangle is the whole of the lengths of its sides Two points measure 42 and 48 shape an integral edge.Slide 26
Symbolic Notations infers Conditional Statement ( p q) If the sun is out, then the climate is great. Banter Statement ( q p) If the climate is great, then the sun is out. p q pSlide 27
Exercise Let p be "the estimations of x is - 5" and let q be "the outright estimation of x is 5". Compose p q in words. Compose q p in words. On the off chance that the estimations of x is - 5, then the supreme estimation of x is 5. On the off chance that the outright estimation of x is 5, then the estimations of x is - 5.Slide 28
Symbolic Notations Conditional Statement ( p q) If the sun is out, then the climate is great. Reverse Statement (~ p ~q) image of refutation (~) If the sun is not out, then the climate is bad. p q ~q ~pSlide 29
In rundown…Slide 30
Law of Detachment Law of Detachment If p q is a genuine restrictive explanation and p is valid, then q is valid. Law of Syllogism If p q and q r are genuine contingent proclamations, then p r is valid.Slide 31
Law of Syllogism If a winged creature is the speediest feathered creature ashore, then it is the biggest of all fowls. On the off chance that a winged creature is the biggest of all feathered creatures, then it is an ostrich. Join two contingent articulations together If a fledgling is the speediest fowl ashore, then it is an ostrich.Slide 32
Review Fill in the case with proper images and illustrations.Slide 33
Review Rewrite the contingent articulation in if-then frame. It must be valid in the event that you read it in a daily paper. On the off chance that you read it in a daily paper, then it must be valid.Slide 34
Review Write the reverse, talk, and contrapositive of the contingent proclamation. On the off chance that you are inside, then you are not gotten in a rainstorm. Opposite: If you are not inside, then you are gotten in a rainstorm. Chat: If you are not gotten in a rainstorm, then you are inside. Contrapositive: If you are gotten in a rainstorm, then you are not inside.Slide 35
Review Using p, q, r and s underneath, compose the typical articulations in words. p: we go shopping. q: we require a shopping list r: we stop at the bank s: we see our companions. p q ~p ~s If we go shopping, then we require a shopping list. In the event that we don\'t go shopping, then we don\'t see our companions.Slide 36
2.4 Reasoning with Properties from Algebra Day 2 Part 2 CA Standard 3.0Slide 37
Algebraic Properties of Equality Addition property: If a=b, then a+c = b+c. Subtraction property: If a=b, then a-c = b-c. Augmentation property: If a=b, then air conditioning = bc. Division property: If a=b, and c≠0, then a/c = b/c.Slide 38
Solve 5x – 18 = 3x + 2 and clarify each progression in composing. 5x – 18 = 3x + 2 2x – 18 = 2 2x = 20 x = 10 Subtraction p. of e. Expansion p. of e. Division p. of e.Slide 39
More properties of equity Reflexive property: For any genuine number an, a=a. Symmetric property: If a=b, then b=a. Transitive property: If a=b and b=c, then a=c. Substitution property: If a=b, then a can be substituted for b in any condition or expression.Slide 40
Example Solve 55z – 3(9z + 12) = - 64 and compose a purpose behind each progression.Slide 41
Properties of EqualitySlide 42
Review Let p be "a shape is a triangle" and let q be "it has an intense point". Compose the contrapositive of p q. Compose the backwards of p q.Slide 43
Review How is the item 4 · 6 identified with 5 2 ? How is the item 5 · 7 identified with 6 2 ? Make a guess about how the result of two positive buries n and n + 2 is identified with the square of the whole number between them. Compose a persuading contention to legitimize your guess.Slide 44
Pg. 91 # 8 – 20 Pg. 92 # 26 – 42 Pg. 99 # 15 – 23, 32Slide 45
2.5 Proving Statements and Segments Day 3 Part 1 CA Standard 2.0, 4.0, 16.0Slide 46
Warmup Identify the property of equity. On the off chance that m<1 = m<2, then m<2 = m<1.Slide 47
Properties of Segment Congruence Segment compatibility is reflexive, symmetric, and transitive. Reflexive: For any portion AB, . Symmetric: If , then . Transitive: If , and , thenSlide 48
Symmetric Property of Segment Congruence Given: PQ XY Prove: XY PQ Statements Reasons 1.PQ XY 1. Given 2.PQ = XY 2. Meaning of consistent portions 3.XY = PQ 3. Symmetric property of correspondence 4.XY PQ 4. Meaning of consistent fragments P X Q YSlide 49
Another case Given: LK = 5, JK = 5, JK JL. Demonstrate: LK JL. Statements Reasons 1._________ 1. Given 2. _________ 2. Given 3. LK = JK 3. Transitive p. o. e 4. LK JK 4. ________________ 5. JK JL 5. Given 6. ________ 6. Transitive p o e LK = 5 JK = 5 Definition of consistent portions LK ≈ JLSlide 51
Solve for the variable utilizing the given data. Clarify your means. Given: . . . . D 2X + 1 B C A 4X - 11Slide 53
2.6 Proving Statements about Angles Day 3 Part 2 CA Standar
A Representation of the Uninsured The Organization for Urban Family Wellbeing Susanne Callahan K ...
MMC Norilsk Nickel Bunch Examined Merged Yearly Money related Explanations 31 December 2003. Jun ...
Authority position in shopper flower class. Developing B2B flower vendor business opportunity .. ...
(I would like a ham sandwich.) Che cosa avremmo dovuto toll? ... The restrictive is additionally ...
Worldwide Internet Conference. Forward-Looking Statements. This presentation contains
Antonio purchased the most extravagant gold chain in the adornments store. ... This shoes store ...
Results for Q3 onwards to be accounted for under new structure. Foundation ... Beforehand report ...
Solid asset report and longstanding adherence to budgetary approaches. Redesigned 2009 merged an ...
presentation to the monetary group. 2Q outcomes tuesday 29th july 2003 ... also, instabilities a ...
... expected future occasions and money related and working results that are liable to character ...
More than 2 million bits of fine gems and 3 million carats of cut stones ... The China gems busi ...
Fall Merchandise Overview & Fashion Show. Q & A with Management. Fall Virtual Store Tour ... Des ...
... in configuration structural engineering; inside outline; beautiful expressions including gem ...
Essential REQUIREMENTS. Put OR ACTIVELY IN PROCESS OF INVESTING$1,000,000$ 500,000 IF TEAFunds
CIS162AD. 2. Review of Topic. Pseudocode Flow Control StructuresFlowchartingIf, If-ElseNested If ...
The principal contingent is a structure utilized for discussing potential outcomes as a part of ...