1003 segment and angle addition postulate and more
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Transcript of 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.
35