1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof ...

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1.3 Segments and Their Measures Geometry

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Transcript of 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof ...

Page 1: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

1.3 Segments and Their MeasuresGeometry

Page 2: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

PostulatesRules that are accepted as true without

proofSometimes they are called axioms.

Page 3: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Postulate 1: Ruler Postulate

Page 4: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Find the the measure measure of of AB.. AA BB

Point A is at 1.5 and B is at 5.

So, AB = 5 - 1 1.5 = 3.55 = 3.5

Example 1

Page 5: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 2Find the measure of PRAns: |3-(-4)|=|3+4|=7Would it matter if I asked for

the distance from R to P ?

Page 6: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Between

Page 7: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Postulate 2: Segment Addition Postulate

Page 8: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 3: DE=2, EF=5, and DE=FG. Find FG, DF, DG, & EG.

Page 9: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 4: Find the length of JT.

Page 10: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Ways to find the length of a segment on the coordinate plane

1) Pythagorean Theorem- Can be used on and off the coordinate plane

2) Distance Formula – only used on the coordinate plane

Page 11: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

1) Pythagorean Theorem** Only can be used with Right TrianglesWhat are the parts to a RIGHT Triangle?1. Right angle2. 2 legs3. Hypotenuse

Right angle

LEG

Leg – Sides attached to the Right angle

Hypotenuse- Side across from the right angle. Always the longest side of a right triangle.

Page 12: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Pythagorean Theorem222 )()()( hypotenuselegleg

222 cba

Page 13: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 5: Find the missing length in the triangle. Find the missing segment- Identify the parts

of the triangle5 in

13 in

Ans: 5 2 + X 2 = 13 2

Leg 2 + Leg 2 = Hyp 2

hyp

Leg

Leg

25 + X 2 = 169

X 2 = 144

X = 12 in

Page 14: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 6: Find the distance of JT(Using the Pythagorean Theorem)

Make a right Triangle out of the segment

(either way)

Find the length of each leg of the right Triangle.

Then use the Pythagorean Theorem to find the Original segment JT (the hypotenuse).

Page 15: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

10

88.12164

164

10064

108

2

2

222

DC

DC

DC

DC

We got 8 by | -4 – 4|

We got 10 by | 6 - - 4|

Example 7: Find the distance of CD

Page 16: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 8: Observe the map to answer the following questions:

Page 17: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

The Distance Formula

Page 18: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values

(4-(-3))2 + (2-(5))2

(4+3)2 + (2-5)2

(7)2 +(-3)2

49+9 =58 ~ 7.6~

J (-3,5) T (4,2)

x1, y1 x2, y2

Example 9: Use the Distance Formula to find JT

Page 19: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 10: Use the distance formula

Find the length of the green segment

Ans: 109 or approximately 10.44

Page 20: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Example 11: Find the lengths of all the segments. Tell whether any of the segments have the same length.

Page 21: 1.3 Segments and Their Measures Geometry. Postulates Rules that are accepted as true without proof Sometimes they are called axioms.

Congruent Segments


Definitions and Postulates

Definitions and Postulates

Axioms of Kemet

Axioms of Kemet

Euclids five postulates

Euclids five postulates

Chapter 4 Congruence of Line Segments, Angles, and … · Segments,and Angles 4-2 Using Postulates and Definitions in Proofs 4-3 Proving Theorems About ... has a midpoint, point M,

Chapter 4 Congruence of Line Segments, Angles, and … · Segments,and Angles 4-2 Using Postulates and Definitions in Proofs 4-3 Proving Theorems About ... has a midpoint, point M,

Separation Axioms

Separation Axioms

Euclid's Five Postulatesmypages.iit.edu/~maslanka/24Prop.pdf · Euclid's Five Postulates These are the axioms of standard Euclidean Geometry. They appear at the start of Book I of

Euclid's Five Postulatesmypages.iit.edu/~maslanka/24Prop.pdf · Euclid's Five Postulates These are the axioms of standard Euclidean Geometry. They appear at the start of Book I of

Quantum Mechanics Postulates

Quantum Mechanics Postulates

Koch's postulates demostration

Koch's postulates demostration

Hilbert Axioms

Hilbert Axioms

Materials- Metals &Non-metals EUCLID’S GEOMETRY...Materials- Metals &Non-metals AXIOMs/COMMON NOTIONS Euclid’s Five Postulates Consistency of System of Axioms Euclid of Alexandria

Materials- Metals &Non-metals EUCLID’S GEOMETRY...Materials- Metals &Non-metals AXIOMs/COMMON NOTIONS Euclid’s Five Postulates Consistency of System of Axioms Euclid of Alexandria

Homework: magic squares€¦ · Euclid's Postulates in his “Elements” (axioms – basic truths) 1. A straight line segment can be drawn joining any two points. 2. Any straight

Homework: magic squares€¦ · Euclid's Postulates in his “Elements” (axioms – basic truths) 1. A straight line segment can be drawn joining any two points. 2. Any straight

Kant on Parallel Lines: Definitions, Postulates, and Axioms...been made of these notes. Erich Adickes, the editor of volume 14 of Kant’s Gesammelte Schriften, has given by far the

Kant on Parallel Lines: Definitions, Postulates, and Axioms...been made of these notes. Erich Adickes, the editor of volume 14 of Kant’s Gesammelte Schriften, has given by far the

CONTROLLING EMOTIONS - Wikimedia Commons · Human All-Too-Human 39 Astonishing functions of human brain and miracles of mind 170 Personal Idealism/Axioms as Postulates 247 The Analysis

CONTROLLING EMOTIONS - Wikimedia Commons · Human All-Too-Human 39 Astonishing functions of human brain and miracles of mind 170 Personal Idealism/Axioms as Postulates 247 The Analysis

1.1 Identify Points, Lines, and Planes · 1.2 Use Segments and Congruence Obj.: Use segment postulates to identify congruent segments. Key Vocabulary • Postulate, axiom - In Geometry,

1.1 Identify Points, Lines, and Planes · 1.2 Use Segments and Congruence Obj.: Use segment postulates to identify congruent segments. Key Vocabulary • Postulate, axiom - In Geometry,

New Axioms

New Axioms

 · Web viewThere are finally simple ideas of which no definition can be given. There are also the axioms and postulates or, in a word, the primary principles which cannot be proved

 · Web viewThere are finally simple ideas of which no definition can be given. There are also the axioms and postulates or, in a word, the primary principles which cannot be proved

Zurich Axioms

Zurich Axioms

Axioms From

Axioms From

CONSUMER PREFERENCE AXIOMS: BEHAVIORAL POSTULATES …

CONSUMER PREFERENCE AXIOMS: BEHAVIORAL POSTULATES …

1.3 Segments and Their Measures Learning Targets: I can use segment postulates. I can use the Distance Formula to measure distances.

1.3 Segments and Their Measures Learning Targets: I can use segment postulates. I can use the Distance Formula to measure distances.