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Warmup. State whether every sentence is genuine or false.If you live in Los Angeles, then you live in California.If you live in California, then you live in Los Angeles.If today is Wednesday, then tomorrow is Thursday.If tomorrow is Thursday, then today is Wednesday. . Genuine. False. Genuine. Genuine. Contingent Statement.

Transcripts

2.1 Conditional Statements Day 1 Part 1 CA Standards 1.0, 3.0

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 True

Conditional Statement Conditional explanation has two sections, speculation and a conclusion. On the off chance that _____________, then____________. speculation conclusion

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.

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.

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 Converse

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.

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 Inverse

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 Contrapositive

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.

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.

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.

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.

Postulate 11 If two planes converge, then their crossing point is a line.

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.

2.2 Definitions and Biconditional Statements Day 1 Part 2 CA Standards 1.0, 3.0

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.

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 . C

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.

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.

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.

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.

Pg. 75 # 4 – 38 even Handout 2.2

2.3 Deductive Reasoning Day 2 Part 1 CA Standards 1.0, 3.0

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.

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 p

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.

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 ~p

In rundown…

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.

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.

Review Fill in the case with proper images and illustrations.

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.

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.

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.

2.4 Reasoning with Properties from Algebra Day 2 Part 2 CA Standard 3.0

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.

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.

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.

Example Solve 55z – 3(9z + 12) = - 64 and compose a purpose behind each progression.

Properties of Equality

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.

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.

Pg. 91 # 8 – 20 Pg. 92 # 26 – 42 Pg. 99 # 15 – 23, 32

2.5 Proving Statements and Segments Day 3 Part 1 CA Standard 2.0, 4.0, 16.0

Warmup Identify the property of equity. On the off chance that m<1 = m<2, then m<2 = m<1.

Properties of Segment Congruence Segment compatibility is reflexive, symmetric, and transitive. Reflexive: For any portion AB, . Symmetric: If , then . Transitive: If , and , then

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 Y

Example

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 ≈ JL

Solve for the variable utilizing the given data. Clarify your means. Given: . . . . D 2X + 1 B C A 4X - 11

2.6 Proving Statements about Angles Day 3 Part 2 CA Standar