measuring segments and coordinate plane
DESCRIPTION
This slideshow was used to introduce application of Segment Addition Postulate along with Coordinate Plane in Geometry. There is a review of several concepts at the end of the two lessons.TRANSCRIPT
![Page 1: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/1.jpg)
1.4: Measuring Segments and Angles
Prentice Hall Geometry
![Page 2: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/2.jpg)
Coordinate :Coordinate : The numerical location of a point on a number line.
Length :Length : On a number line length AB = AB = |B - A|
Midpoint :Midpoint : On a number line, midpoint of AB = 1/2 (B+A)
BA C D E
2 4 6 8-2-4-6-8 -1 0
![Page 3: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/3.jpg)
Find the length of each segment.
XY = | –5 – (–1)| = | –4| = 4
ZY = | 2 – (–1)| = |3| = 3
ZW = | 2 – 6| = |–4| = 4
Find which two of the segments XY, ZY, and ZW are
congruent.
Because XY = ZW, XY ZW.
GEOMETRY LESSON 1-4GEOMETRY LESSON 1-4
Measuring Segments and AnglesMeasuring Segments and Angles
![Page 4: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/4.jpg)
The Segment Addition PostulateThe Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C,
then AB + BC = AC.
A B C
![Page 5: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/5.jpg)
Use the Segment Addition Postulate to write an equation.
AN + NB = AB Segment Addition Postulate(2x – 6) + (x + 7) = 25 Substitute.
3x + 1 = 25 Simplify the left side. 3x = 24 Subtract 1 from each side. x = 8 Divide each side by 3.
AN = 10 and NB = 15, which checks because the sum of the segment lengths equals 25.
If AB = 25, find the value of x. Then find AN and NB.
AN = 2x – 6 = 2(8) – 6 = 10 NB = x + 7 = (8) + 7 = 15 Substitute 8 for x.
![Page 6: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/6.jpg)
Use the definition of midpoint to write an equation.
5x + 45 = 8x Add 36 to each side.
RM and MT are each 84, which is half of 168, the length of RT.
M is the midpoint of RT. Find RM, MT, and RT.
RM = 5x + 9 = 5(15) + 9 = 84MT = 8x – 36 = 8(15) – 36 = 84
Substitute 15 for x.
RT = RM + MT = 168
RM = MT Definition of midpoint5x + 9 = 8x – 36 Substitute.
45 = 3x Subtract 5x from each side. 15 = x Divide each side by 3.
![Page 7: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/7.jpg)
1. T is in between of XZ. If XT = 12 and XZ = 21,
then TZ = ?
2. T is the midpoint of XZ. If XT = 2x +11 and XZ = 5x + 8,
find the value of x.
Quiz
![Page 8: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/8.jpg)
Coordinate Plane
![Page 9: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/9.jpg)
Parts of Coordinate Plane
x-axis
y-axis
origin
Quadrant IQuadrant II
Quadrant IVQuadrant III
( +, + )( - , + )
( - , - )( + , - )
![Page 10: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/10.jpg)
DistanceDistanceOn a number line
formula: d = | x2 – x1 |
On a coordinate plane
formula:
212
21 )()(
2yyxxd
![Page 11: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/11.jpg)
Find the distance between T(5, 2) and R( -4. -1) to the nearest tenth.
Find the distance between T(5, 2) and R( -4. -1) to the nearest tenth.
AB has endpoints
A (1, -3) and B (-4, 4).
Find AB to the nearest tenth.
![Page 12: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/12.jpg)
MidpointMidpoint
On a number line
formula: 2
ba
On a coordinate plane
formula:
2
,2
, 2121 yyxxyx mm
![Page 13: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/13.jpg)
QS has endpoints Q(3, 5) and S(7, -9).
Find the coordinates of its midpoint M.
The midpoint of AB is M(3, 4). One endpoint is A(-3, -2).
Find the coordinates of the other endpoint B.
![Page 14: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/14.jpg)
FAD , FBC, 1 • Right Angle• Obtuse Angle• Acute Angle• Straight Angle• Congruent Angles
• Formed by two rays with the same endpoint. • The rays: sides• Common endpoint: the vertex• Name:
• Measures exactly 90º• Measure is GREATER than 90º• Measure is LESS than 90º• Measure is exactly 180º ---this is a line• Angles with the same measure.
1
2
FAD
ADE
FAB
• Angles
![Page 15: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/15.jpg)
Name the angle below in four ways.
The name can be the vertex of the angle: G.
Finally, the name can be a point on one side, the vertex, and a point on the other side of the angle:
AGC, CGA.
The name can be the number between the sides of the angle: 3
![Page 16: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/16.jpg)
Use the Angle Addition Postulate to solve.
m 1 + m 2 = m ABC Angle Addition Postulate.
42 + m 2 = 88 Substitute 42 for m 1 and 88 for m ABC.
m 2 = 46 Subtract 42 from each side.
Suppose that m 1 = 42 and m ABC = 88. Find m 2.
![Page 17: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/17.jpg)
Use the figure below for Exercises 4–6.
4. Name 2 two different ways.
5. Measure and classify 1, 2, and BAC.
6. Which postulate relates the measures of 1, 2, and BAC?
14
Angle Addition Postulate
Use the figure below for Exercises 1-3.
1. If XT = 12 and XZ = 21, then TZ = 7.
2. If XZ = 3x, XT = x + 3, and TZ = 13, find XZ.
3. Suppose that T is the midpoint of XZ. If XT = 2x + 11 and XZ = 5x + 8, find the value of x.
9
24
90°, right; 30°, acute; 120°, obtuse
DAB and BAD
![Page 18: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/18.jpg)
Homework
Page 56 # 2, 4, 18, 20, 24, 26
![Page 19: Measuring Segments and Coordinate Plane](https://reader035.vdocuments.net/reader035/viewer/2022062319/5559cbe4d8b42a93208b4889/html5/thumbnails/19.jpg)
REVIEW!
Page 71 # 1- 16Page 72 # 19- 31
Page 73 # 34- 38