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GEOMETRY CHAPTER 2 2-4: Use Postulates and Diagrams

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Page 1: Geometry Chapter 2 - rgeometry16-17.weebly.comrgeometry16-17.weebly.com/uploads/8/6/1/2/86123628/2-4_use... · –Postulate 3: Protractor Postulate –Postulate 4: Angle Addition

GEOMETRY CHAPTER 22-4: Use Postulates and Diagrams

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Warm-Up

■ State which postulate justifies each statement

1.) If 𝑫 is the interior of < 𝑨𝑩𝑪, then

𝒎 < 𝑨𝑩𝑪 = 𝒎 < 𝑨𝑩𝑫 +𝒎 < 𝑫𝑩𝑪

2.) A protractor was used to find the measure of an

angle to be 𝟏𝟐𝟓°

3.) If M is between X and Y, then

𝐗𝐌+𝐌𝐘 = 𝐗𝐘

Angle Addition Postulate

Protractor Postulate

Segment Addition Postulate

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2-4: Use Postulates and Diagrams

■ Objective: Students will be able to know and

use postulates related to points, lines and

planes.

■ Agenda

– Postulates (Old and New)

– Practice

– Sketches

– Interpreting

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Basic Terms

■ Postulate: A basic assumption that is accepted without proof.

■ Exists: There is at least one.

■ Unique: There is no more than one.

■ One and only one: There is exactly one.

■ Determine: To decline or specify.

■ Theorem: A statement that can be proved using postulates,

definitions, and previously used theorems.

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Postulates

■ In chapter 1, we covered 4 postulates

– Postulate 1: Ruler Postulate

– Postulate 2: Segment Addition Postulate

– Postulate 3: Protractor Postulate

– Postulate 4: Angle Addition Postulate

■ Here are seven new postulates

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Postulate #1

■ The Ruler Postulate:

– The Distance between points A and B, named AB, is equal

to the absolute value of the difference of the coordinates

of A and B.

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Postulate #2

■ Segment Addition Postulate:

If B is between A and C, then 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶.

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Postulate #3

■ The Protractor Postulate:

The measure of < 𝑨𝑶𝑩 is equal to the absolute value of the difference between the

real numbers for 𝑶𝑨 and 𝑶𝑩.

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Postulate #4

■ The Angle Addition Postulate:

If 𝑷 is the interior of < 𝑹𝑺𝑻, then 𝒎 < 𝑹𝑺𝑻 = 𝒎 < 𝑹𝑺𝑷 +𝒎 < 𝑷𝑺𝑻

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New Postulates – Pg 88 (Textbook)

■ Postulate #5:

Through any two points their exists exactly one line

■ Postulate 6:

A line contains at least two points

A B

A Bm

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New Postulates – Pg 88 (Textbook)

■ Postulate #7:

If two lines intersect, then their intersection is exactly

one point.

■ Postulate #8:

Through any three noncollinear points their exists

exactly one plane.

m

n

A

A

B C

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New Postulates – Pg 88 (Textbook)

■ Postulate #9:

A plane contains at least three noncollinear points.

■ Postulate 10:

If two points lie in a plane, then the line containing

them is also in the plane.

A

B C

D

AB

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New Postulates – Pg 88 (Textbook)

Postulate 11:

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

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State the Postulate is being illustrated by the diagram.

1.) 2.)

Practice With Postulates

Postulate 8Postulate 10

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State the Postulate illustrated by the diagram.

3.)

Practice With Postulates

If

Postulate 7

Then

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State the Postulate illustrated by the diagram.

4.)

Practice With Postulates

Postulate 11

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Sketch a diagram showing 𝑻𝑽intersecting 𝑷𝑸 at point 𝑾, so that

𝑻𝑾 ≅ 𝑾𝑽

You can sketch the diagram using the

following steps:

Step 1: Draw 𝑻𝑽 and label points T

and V

Step 2: Draw point W at the midpoint

of 𝑻𝑽, and mark the congruent

segments

Step 3: Draw 𝑷𝑸 through 𝑾

Sketch a Diagram

T

V

W

P

Q

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Perpendicular Figures

A line is a line perpendicular to a plane if and only if the line intersects

the plane in a point and is perpendicular to every line in the plane that

intersects it at that point.

A m

p

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Interpreting a Diagram

Which of the following statements

cannot be assumed from the

diagram?

A, B, and F are collinear

E, B, and D are collinear

𝐴𝐵 ⊥ 𝑝𝑙𝑎𝑛𝑒 𝑆

𝐶𝐷 ⊥ 𝑝𝑙𝑎𝑛𝑒 𝑇

𝐴𝐹 intersects 𝐵𝐶 at point B

Cannot be assumed (Why?)

Cannot be assumed (Why?)

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Extra Practice

■ Sketch Diagrams to Illustrate the following:

𝑳𝑵, 𝑨𝑩, and 𝑫𝑪 intersecting at point M, 𝑨𝑩 bisecting 𝑳𝑵,

and 𝑫𝑪 ⊥ 𝑳𝑵.

L NM

A

B

D

C

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HW 2-4

■ Pg. 91-94

■ #’s 3 – 10, 14 – 24, 27, 30 – 32, 35 – 38

■ (EC) 11 – 13