2-5 Reasoning in Algebra and Geometry. Properties of Equality.
-
Upload
richard-parker -
Category
Documents
-
view
213 -
download
1
Transcript of 2-5 Reasoning in Algebra and Geometry. Properties of Equality.
![Page 1: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/1.jpg)
2-5 Reasoning in Algebra and Geometry
![Page 2: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/2.jpg)
Properties of Equality
![Page 3: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/3.jpg)
The Distributive Property
![Page 4: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/4.jpg)
Problem 1: Justifying Steps when Solving an Equation
What is the value of x? Justify each step
1) 180
2)2 30 180
3)3 30 180
4)3 150
5) 50
AOM MOC
x x
x
x
x
![Page 5: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/5.jpg)
Problem 1: Justifying Steps when Solving an Equation
What is the value of x? Justify each step
1) 2 75
2) 75
3) 75
x x
x
x
![Page 6: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/6.jpg)
Properties of Congruence
![Page 7: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/7.jpg)
Problem 2: Using Properties of Equality and Congruence
What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?
![Page 8: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/8.jpg)
What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?
![Page 9: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/9.jpg)
What is the name of the property of equality or congruence that justifies going from the 1st statement to the second statement?
![Page 10: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/10.jpg)
Proof: a convincing argument that uses deductive reasoning (shows why a conjecture is true)
Two-Column Proof: lists each statement on the left and the justification or reason for each statement on the right. Each step must follow logically from the steps before it.
![Page 11: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/11.jpg)
![Page 12: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/12.jpg)
Problem 3: Writing a Two-Column Proof
1) 1 3
2) 2 2
3) 1 2 3 2
4) 1 2
3 2
5)
m m
m m
m m m m
m m AEC
m m DEB
m AEC m DEB
![Page 13: 2-5 Reasoning in Algebra and Geometry. Properties of Equality.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dac5503460f94a9c2eb/html5/thumbnails/13.jpg)
1)
2)
3)
4)
5)
6)
7)
AB CD
AB CD
BC BC
AB BC BC CD
AB BC AC
BC CD BD
AC BC
AC BC