Download - Section 2-4: Reasoning in Algebra
![Page 1: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/1.jpg)
Section 2-4: Reasoning in Algebra
Goal 2.01: Use logic and deductive reasoning to draw
conclusions and solve problems.
![Page 2: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/2.jpg)
Turn in Homework
• Lesson Quiz 2-3
![Page 3: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/3.jpg)
Essential Question
How are properties of equality used in Algebraic and Geometric Proofs?
![Page 4: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/4.jpg)
Addition Property of Equality
If a = b and c = d, then a + c = b + d.
![Page 5: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/5.jpg)
subtraction property of equality
If a = b and c = d, then a – c = b – d.
![Page 6: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/6.jpg)
multiplication property of equality
If a = b then ac = bc.
![Page 7: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/7.jpg)
division property of equality
If a = b and c ≠ 0, then a = b . c c
![Page 8: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/8.jpg)
substitution property
If a = b then either a or b may be substituted for the other in any equation or inequality.
![Page 9: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/9.jpg)
reflexive (identity) Property
a = a
DE = DE
1 = 1
![Page 10: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/10.jpg)
Symmetric Property
If a = b then b = a.
![Page 11: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/11.jpg)
Distributive Property
a ( b + c ) = ab + ac
a ( b – c) = ab - ac
![Page 12: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/12.jpg)
Transitive Property
If a = b and b = c, then a = c.
If DE = FG and FG = JK, then DE = JK.
If 1 = 2 and 2= 3, then 1 = 3.
![Page 13: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/13.jpg)
Midpoint Theorem
If M is the midpoint of AB, then AM = ½ AB and MB = ½ AB, also 2 AM = AB and 2MB = AB.
![Page 14: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/14.jpg)
Angle Bisector Theorem
If BX is the bisector of ABC, then
2 m ABX = m ABC and m ABX = m ABC.
2 m XBC = m ABC and m XBC = m ABC.
![Page 15: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/15.jpg)
Review:
Definition of midpointDefinition of angle bisectorAngle Addiction PostulateSegment Addition Postulate
![Page 16: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/16.jpg)
• Compare the definition of midpoint to the Midpoint Theorem?
![Page 17: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/17.jpg)
• Compare the definition of the angle bisector and the Angle Bisector Theorem?
![Page 18: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/18.jpg)
Examples
• Worksheet Labeled: Justify the Statements examples
• Together: p 92 (5 – 24 all)
![Page 19: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/19.jpg)
Group Work
Practice 2-4 2 – 14 evens
![Page 20: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/20.jpg)
Individual Work
Practice 2-4: 1 – 13 odds
![Page 21: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/21.jpg)
Assess
Lesson Quiz 2 – 4: for a grade
![Page 22: Section 2-4: Reasoning in Algebra](https://reader035.vdocuments.us/reader035/viewer/2022062502/568156c7550346895dc459aa/html5/thumbnails/22.jpg)
Homework
Worksheet back on Front:
Labeled: Properties of Algebra Justify the Statement Homework