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

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

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

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

POSTULATE 11: If two planes intersect, then their intersection is a line.

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.

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.

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

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

2.5 Algebraic Properties

Addition property

Subtraction property

Multiplication property

Division Property

Substitution property

Distribution property

Combine like terms

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

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

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

ALGEBRAIC PROOF:

Statement

Reason

Given: Prove:

1. 1. Given.

2. 2. Subtraction Property

3. 3. Division Property

ALGEBRAIC PROOF:

Statement

Reason

Given: Prove:

1. 1. Given.

2. 2. Subtraction Property

3. 3. Division Property

PROOFS WITHOUT THE “WORK”

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

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”

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

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”

PROPERTIESREAL

NUMBERS SEGMENTS ANGLESREFLEXIVE

SYMMETRIC

TRANSITIVE

“equals itself”

“same in reverse”

“there’s a middle man”

SOLUTIONS:4. SYMMETRIC PROPERTY5. TRANSITIVE PROPERTY6. REFLEXIVE PROPERTY