TODAY IN GEOMETRY… Learning Goal 1: 2.4 You will use postulates involving points, lines, and...
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![Page 1: TODAY IN GEOMETRY… Learning Goal 1: 2.4 You will use postulates involving points, lines, and planes Independent Practice – 20 minutes! Learning Goal.](https://reader038.fdocuments.us/reader038/viewer/2022102808/56649d965503460f94a7eb40/html5/thumbnails/1.jpg)
TODAY IN GEOMETRY…
Learning Goal 1: 2.4 You will use postulates involving points, lines, and planes
Independent Practice – 20 minutes!
Learning Goal 2: 2.5 Use Algebraic properties to form logical arguments
Test Retakes before next Friday
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POSTULATE 5: POSTULATE 6: Through any two points there exists one line.
A line contains at least two points.
𝐴
𝐵
𝐶
𝐴
𝐵
𝐶𝐷
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POSTULATE 7: POSTULATE 8: If two lines intersect, then their intersection is exactly one point.
Through any three noncollinear points there exists exactly one plane.
𝐴
𝐴
𝐵𝐶
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POSTULATE 9: POSTULATE 10: A plane contains at least three noncollinear points.
If two points lie in a plane, then the line containing them lies in the plane.
𝐸
𝐹𝐺
𝐻𝐼
𝐺
𝐻
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POSTULATE 11: If two planes intersect, then their intersection is a line.
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PRACTICE: State the postulate illustrated by the diagram.
POSTULATE 7:If two lines intersect, then their intersection is exactly
one point.
POSTULATE 11:If two planes intersect, then their intersection is a line.
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PRACTICE: Use the diagram to write examples of each postulate:
POSTULATE 9:
POSTULATE 10:
A plane contains at least three noncollinear points.
Plane P contains points noncollinear points B, A, C
If two points lie in a plane, then the line containing them lies in the plane.
Points A and B lie on Plane P, line n also lies on Plane P.
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PRACTICE: Use the diagram to determine if the statement is true or false.1. All points are coplanar.
2. G, F, and E are collinear.
3. and intersect.
4. and are vertical angles.
5. and intersect at H.
6.
T
F
F
T
T
F
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20 minutesHOMEWORK #2:
Pg. 99: 3-8, 11-23
If finished, work on other assignments:
HW #1: Pg. 82: 3-18, 26-28, 47-54
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2.5 Algebraic Properties
Addition property
Subtraction property
Multiplication property
Division Property
Substitution property
Distribution property
Combine like terms
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ADDITION PROPERTY: SUBTRACTION PROPERTY:Use when you must
add to solve an algebraic problem.
Use when you must subtract to solve an algebraic problem.
EXAMPLE: If , then
EXAMPLE: If , then
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MULTIPLICATION PROPERTY:
DIVISION PROPERTY: Use when you must multiply to solve an algebraic problem.
Use when you must divide to solve an algebraic problem.
EXAMPLE: If , then
EXAMPLE: If , then
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SUBSTITUTION PROPERTY:
DISTRIBUTIVE PROPERTY:
COMBINE LIKE TERMS: Use
when you must substitute to solve an algebraic problem.
EXAMPLE: If , then
Use when you must distribute to solve an algebraic problem.
Use when you must combine like terms to solve an algebraic problem.
EXAMPLE: If , then
EXAMPLE: If , then
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Subtraction Property
3. 3. Division Property
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Subtraction Property
3. 3. Division Property
PROOFS WITHOUT THE “WORK”
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Distribution Property
3. 3. Addition Property+8+8
−4 (11𝑥 )+ (−4 ) (2 )=80
4. 4. Division Property
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Distribution Property
3. 3. Addition Property
4. 4. Division Property
PROOFS WITHOUT THE “WORK”
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Distribution Property
4. 4. Subtraction Property−3−3
2 (𝑥 )+(2 ) (5 )−7=19
5. 5. Division Property
2 𝑥+(10−7 )=193. 3. Combine like terms
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ALGEBRAIC PROOF:
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Distribution Property
4. 4. Subtraction Property
5. 5. Division Property
3. 3. Combine like terms
PROOFS WITHOUT THE “WORK”
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PROPERTIESREAL
NUMBERS SEGMENTS ANGLESREFLEXIVE
SYMMETRIC
TRANSITIVE
“equals itself”
“same in reverse”
“there’s a middle man”
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SOLUTIONS:4. SYMMETRIC PROPERTY5. TRANSITIVE PROPERTY6. REFLEXIVE PROPERTY