1 3 segments and their measures
This presentation is the property of its rightful owner.
Sponsored Links
1 / 15

1.3 Segments and Their Measures PowerPoint PPT Presentation


  • 57 Views
  • Uploaded on
  • Presentation posted in: General

1.3 Segments and Their Measures. Objectives/Assignment. Use segment postulates. Use the Distance Formula to measure distances as applied. Using Segment Postulates.

Download Presentation

1.3 Segments and Their Measures

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


1 3 segments and their measures

1.3 Segments and Their Measures


Objectives assignment

Objectives/Assignment

  • Use segment postulates.

  • Use the Distance Formula to measure distances as applied.


Using segment postulates

Using Segment Postulates

  • In geometry, rules that are accepted without proof are called postulates, or axioms. Rules that are proved are called theorems. In this lesson, you will study two postulates about the lengths of segments.


Postulate 1 ruler postulate

The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point.

The distance between points A and B written as AB, is the absolute value of the difference between the coordinates of A and B.

AB is also called the length of AB.

Names of points

A

B

x1

x2

Coordinates of points

Postulate 1: Ruler Postulate

A

AB

B

x1

x2

AB = |x2 – x1|


Ex 1 finding the distance between two points

Measure the length of the segment to the nearest millimeter.

Solution: Use a metric ruler. Align one mark of the ruler with A. Then estimate the coordinate of B. For example if you align A with 3, B appears to align with 5.5.

The distance between A and B is about 2.5 cm.

Ex. 1: Finding the Distance Between Two Points

AB = |5.5 – 3| = |2.5| = 2.5


1 3 segments and their measures

Note:

  • It doesn’t matter how you place the ruler. For example, if the ruler in Example 1 is placed so that A is aligned with 4, then B align 6.5. The difference in the coordinates is the same.


1 3 segments and their measures

USING SEGMENT POSTULATES

Finding the Distance on a Number Line

Find AB, BA, CB, BC, BD, and DB

Solutions:

AB = 1.5, BA = 1.5, CB = 3, BC = 3, BD = 5, DB = 5


1 3 segments and their measures

When three points lie on a line, you can say that one of them is between the other two. This concept applies to collinear points only. For instance, in the figures on the next slide, point B is between points A and C, but point E is not between points D and F.

Note:

A

Point B is between points A and C.

B

C

D

E

Point E is NOT between points D and F.

F


Postulate 2 segment addition postulate

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

Postulate 2: Segment Addition Postulate

AC

A

B

C

AB

BC


1 3 segments and their measures

USING SEGMENT POSTULATES

In the diagram, AD = 34, BC = 14, CD = 13 and AB = BE = EC.

Find BE, EC, AB, AE, ED, and BD

Solution: BE = 7, EC = 7, AB = 7, AE = 14, ED = 20, and BD = 27


1 3 segments and their measures

The Distance Formula

  • The distance d between two points (x1,y1) and (x2,y2) is given by

B(x2, y2)

A(x1, y1)


1 3 segments and their measures

USING THE DISTANCE FORMULA

What is the Distance Formula based on?

B(x2, y2)

| y2 – y1 |

| x2 – x1 |

C(x2, y1)

A(x1, y1)

Pythagorean Theorem

c2 = a2 + b2

D =


1 3 segments and their measures

USING THE DISTANCE FORMULA

Find the distance between the points X(2, -5) and Y(- 4, - 9)

Solution:


1 3 segments and their measures

Classwork p. 21-22 #19, 31, 35, 37, 41


1 3 segments and their measures

p. 21-22 #14 -42, 46, 60-70 Evens


  • Login