1003 segment and angle addition postulate and more

Hon Geom

Take out any paper work you may still have for me.

Put HW on the corner of your desk

1. If x + 2 = 8, then (x + 1)2 = ?

A) 25 B) 36 C) 49 D) 64 E) 80

Geometry Drill 9/3/14#2

Geometry Drill

2. If 5 – y = 1, then y2 – y = ?

A) 4 B) 6 C) 8 D) 10 E) 12

How many points determine a plane?

Are C, Z, and A coplanar?

Objective:To define more key words in geometryTo identify & use the Segment Addition

Postulate and the ruler postulateTo measure angles using a protractorTo identify & use the Angle Addition

Postulate

Key Terms

AngleVertexStraight AngleAdjacent Angles

Congruent Angles

Angle BisectorAngle Addition

PostulateProtractor

Postulate

adjacent angles

linear pair

complementary angles

supplementary angles

vertical angles

Vocabulary

Vocabulary

Length- The distance from one to zero

VOCABULARY LIST

MIDPOINT- THE POINT THAT DIVIDES A SEGMENT INTO TWO CONGRUENT SEGMENTS

Vocabulary

Segment Bisector- A line, segment, ray, or plane that intersects the segment at it midpoint

The Ruler Postulate

1. Two points on a line can be paired with the real numbers in such a way that any two points can have coordinate 0 and 1

2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

Vocabulary

AB means the measure of ABAB=|a-b| or |b-a|.

A B

3 6

TRY THIS

Find the length of AC

A B C

15 7

Find the length of AC

A BC

The length of AB is 32

5

Segment Addition PostulateIf point R is between points P and Q, then

PR+ RQ = PQ

Find the value of Y

1)GE = y, EH = y–1, GH =11

2) GE = 3y, EH = 24, GH =7y – 4

G E H

Find the value of Y

3) GE = y+2, EH = 2y–6, GH =20. Is E the midpoint of GH ?

????????What unit do we use to measure angles?

What instrument do we use to measure angles?

VOCABULARY LIST

Straight ANGLE - AN ANGLE WHO’S MEASURE IS EQUAL 180 DEGREES

VocabularyCongruent Angles-Angles that have the same measure.

40º40º

VOCABULARY LIST

ADJACENT ANGLES - TWO ANGLES IN A PLANE THAT HAVE A COMMON VERTEX AND A COMMON SIDE BUT NO COMMON INTERIOR POINTS

NotationThe measure of a angle ABC is

ABCm

Protractor Posutlate

The measure of a angle <ABC is

|a-b| or |b-a|.a b

Angle Addition Postulate

If point S is in the interior of < PQR, then

PQRmSQRmPQSm

Fine the Values of <A + < B and then define Complimentary

Complimentary

68,22

37,53

60,30

45,45

BA

BA

BA

BA

Not Complimentary

58,12

37,63

60,20

45,47

BA

BA

BA

BA

Fine the Values of <A + < B and then define Supplementary

Supplementary

98,82

90,90

50,130

35,145

BA

BA

BA

BA

Not Supplementary

98,92

90,80

50,150

25,145

BA

BA

BA

BA

Many pairs of angles have special relationships. Some relationships are because of the measurements of the angles in the pair. Other relationships are because of the positions of the angles in the pair.

VocabularyComplementary Angles -

Two angles whose sum is 90 degrees.

VocabularySupplementary Angles -

Two angles whose sum is 180 degrees.

Write the complement1) 15º

2) 87º

3) xº

Write the supplement1) 25º

2) 107º

3) xº

????????????????Are supplementary angles a linear pair?

Vertical AnglesThe opposite angles formed when two lines intersect

1

2

3

4

Vertical Angle Theorem

Vertical angles are congruent

Classify each angle as acute, right, or obtuse.

1. XTS

2. WTU

3. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Find mLMN.

64°

acute

right

32°

4. BD bisects ABC, mABD = , and

mDBC = (y + 4)°. Find mABC.

5. mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find the value of x.

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