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1.4: Measuring Segments and Angles Prentice Hall Geometry

Measuring Segments and Coordinate Plane

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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.

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Page 1: Measuring Segments and Coordinate Plane

1.4: Measuring Segments and Angles

Prentice Hall Geometry

Page 2: Measuring Segments and Coordinate Plane

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

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

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

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

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

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

Coordinate Plane

Page 9: Measuring Segments and Coordinate Plane

Parts of Coordinate Plane

x-axis

y-axis

origin

Quadrant IQuadrant II

Quadrant IVQuadrant III

( +, + )( - , + )

( - , - )( + , - )

Page 10: Measuring Segments and Coordinate Plane

DistanceDistanceOn a number line

formula: d = | x2 – x1 |

On a coordinate plane

formula:

212

21 )()(

2yyxxd

Page 11: Measuring Segments and Coordinate Plane

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

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

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

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

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

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

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

Homework

Page 56 # 2, 4, 18, 20, 24, 26

Page 19: Measuring Segments and Coordinate Plane

REVIEW!

Page 71 # 1- 16Page 72 # 19- 31

Page 73 # 34- 38