angle pair
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Angle PairTRANSCRIPT
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Division of Pasig City and San Juan
SAGAD HIGH SCHOOL
E. Angeles St., Sagad Pasig City
STRATEGIC INTERVENTION MATERIALS
IN
MATHEMATICS III
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NENET M. PENARANDA
Head Teacher III - Math
LAZARO P. TORRES
Principal
LIGAYA G. INSIGNE
Education Supervisor I Secondary Math
Prepared and Submitted by:
FEMILA R. PALICAN
EDWIN P. PECO
HELEN U. RAYMUNDO
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ourney to the World of
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What have you observed on the figure
on the board ?
What kind of angles
are formed ?
The
figure
formeda pair
of
angles
Vertical
Angles are
formed by
intersectinglines
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EXPLORE:
Prepare a whole sheet of paper. You can
make a model of different pairs of angle by
folding a rectangular or square paper, byfolding it lengthwise, cross-wise and
diagonally. The folded corner provides a
convenient model of pair of angles.
From the model figure using a pieceof paper, the broken lines are the folded
crease on the paper. The pairs of angles are
a. supplementary angles
b. complementary angles
c. adjacent angles
d. linear pair
e. vertical angles
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In geometry, pairs of angles are related to each other in several ways. Some
examples are complementary angles, supplementary angles, vertical angles, adjacent
anglesand linear pair.
Two angles are called complementary angles if the sum of their degree measurements equals 90
degrees. One of the complementary angles is said to be the complementof the other.
ABCis the complement of CBD
Two angles are called supplementary angles if the sum of their degree measurements equals 180
degrees. One of the supplementary angles is said to be the supplementof the other.
ABCis the supplement of CBD
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Two pairs of angles are formed by two intersecting lines. Vertical anglesare opposite angles in such an
intersection. Vertical angles are equal to each other.
Very often, math questions will require you to work out the values of angles given in diagrams byapplying the relationships between the pairs of angles.
Example 1: Given the diagram below, determine the values of the anglesx, y and z.
A B
O
C D
Solution:
Step 1:x is a supplement of 65.
Therefore,x+ 65=180x= 18065= 115
Step 2: zand 115are vertical angles.
Therefore, z= 115
Step 3: yand 65are vertical angles.
Therefore, y= 65
Answer:x= 115, y= 65and z= 115
http://www.onlinemathlearning.com/pairs-of-lines.htmlhttp://www.onlinemathlearning.com/pairs-of-lines.html -
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Two angles which are adjacent and whose non common side are opposite rays and formed a
straight line are called linear pair.
D
DEF and DEG are linear pair
25 155
F E G
Two coplanar angles with a common side and a common vertex but, no common interior points.
HIJ and JIK are adjacent angles. H
j
I K
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1. Theorem 1 - 1 VERTICAL ANGLES vertical angles are congruent.
1 and 2 are vertical angles, show that 1 2.
* Angle Addition Postulate *1 m1 + m3 = 180, m2 + m3 = 180
3 4 by substitution, m1 + m3 = m2 + m3
2 Subtract m3 from each side you will get
m1 = m2, m1 m2 or 1 2.
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2. Theorem 1 - 2 If two angles are supplements of congruent angles, then the angles
are congruent.
1 2 3
1 and 2 are supplementary
3 and
2 are supplementaryshow 2 3
1 and 2 are supplementary, m1 + m2 = 180
3 and 2 are supplementary, m3 + m2 = 180
So m1 + m2 = m3 + m3
m1 = m3, m1 m3, 1 3
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3. Theorem 1 3 If two angles are complements of congruent angles, then the two
angles are congruent.
2
1 3
1 and 2 are complementary
3 and 2 are complementary
show 2 3
1 and 2 are complementary, m1 + m2 = 90
3 and 2 are complenmentary, m3 + m2 = 90
So m
1 + m
2 = m
3 + m
3 m1 = m3, m1 m3, 1 3
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1. 2.
1 2
1 2
3. 30 4.
150 50
40
Activity 1Identify the following pair of
angles
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b. Activity # 2
Find the measure of the following angles:
1. m1 = _______
m2 = _______
2
1 30
2. x = ___________
4x = __________
5x = __________5x 4x
x
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3.
x = ___________
1 m 1 = _________
(x + 10) 3 4 (4x 35) m 2 = _________ 2
m 3 = _________
m 4 = _________
4.
x = ____________
m1 = __________
(12x 7) 1 2 (3x - 8) m2 = __________
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5.
(4x + 5)
1
2 (3x + 8)
m 1 = ____________
m 2 = ____________
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c. Activity # 3
SOLVE:
1. The measure of a supplement of 1 is six times the
measure of a complement of 1. Find the measure of 1, its
supplement, and its complement.
2. A and B are supplementary angles andmA = 3x + 12 and mB = 2x 22. Find the measure of both
angles.
3. One angle is twice as large as its complement. Find
the measure of both angles.
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T
a. b.
3 1 2 4 P O Q
c. V
W Z
R S T
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X =
E C m1 = 2x + 6B m2 = 3x + 10
m3 = x + 20
mADE = 24x
3 1
2
D
A
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a.
x = _____, y = _____
1
(3x + 8 ) 2 3 (5x 20) m1 = ________
4 m2 = ________
(5x + 4y) m3 = ________
m4 = ________
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b.
m1 = _____________
2 m2 = _____________
1
25
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1.
2.
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A ti it C d
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Activity Card
Activity Card 1 Activity Card 3
1. Vertical Angle 1. m 1 = 72
2. Supplementary Angle, Linear Pair complement = 18
3. Supplementary Angle supplement = 108
4. Complementary Angle 2.. mA = 126
5. Adjacent Angle m B = 54
3. x, 2(90-x) Activity Card 2 x = 60 , complement = 30
1. m1=90 Assessment Card
m2=60 4. x = 2
2. x =18 m 1 = 10
4x =72 m 2 = 16
5x = 90 m 3 = 22
3. x=15 m
ADE = 48m1=155 Enrichment Card
m3=25 a. x = 14
m2=155 m 1 = 130
m4=25 m 2 = 50
4. x = 13 m 3 = 50
m 1 = 149 m 4 = 130
m 2 = 31 b. m 1 = 90
5. m 1 = 49 m 2 = 65m 2= 41
Activity 4
a. 1 and 3, 2 and 4 are supplementary, linear pair and adjacent
b. TOQ and QOV, QOV and VOP ,VOP and POT, POT and TOQ are allright angles and supplementary angles
c. WSZ and ZST are complementary angles while RSZ and ZST aresupplementary
.
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a. Geometry Activity Book for Enhancement
Skills by Ligaya G. Insigne
b. Geometry by Prentice Hall
c. Geometry by Edwin Moise
d. Geometry by Houghliton Mitten
e. Google and Mozila Firefox