Angles in Intersecting and Parallel Lines

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Angles in Intersecting and Parallel Lines

• Form 1 Mathematics Chapter 10

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Reminder

• Lesson requirement
• Textbook 1B
• Workbook 1B
• Notebook
• Before lessons start
• Desks in good order!
• No rubbish around!
• No toilets!
• Keep your folder at home
• Prepare for Final Exam

3
Reminder

• Missing HW
• Detention
• Ch 11 Ch 12 OBQ Correction
• 24 May (Fri)
• Ch 11 Ch 12 CBQ Correction and signature
• 24 May (Fri)

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Types of Angles(Book 1A p.229) Revision
Acute angle Right angle Obtuse angle

(larger than 0 but smaller than 90)
(equal to 90)
(larger than 90 but smaller than 180)
Straight angle Reflex angle Round angle

(equal to 180)
(larger than 180 but smaller than 360)
(equal to 360)
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Types of Angles(Book 1A p.229) Revision
Classify the angles below.
acute angle ________ right angle
________ obtuse angle _______ straight angle
______ reflex angle ________ round angle
________
A, D
C
B, G
I
F, H
E
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Relation between lines(Book 1A p.231-232)
Revision
2. PQ and RS lie in the same plane and intersect
at 90. We say that they are a pair of
perpendicular lines, or PQ is perpendicular to
RS. In symbols, we write PQ ? RS.
1. AB and CD lie in the same plane and they never
meet. We say that they are a pair of parallel
lines, or AB is parallel to CD. In symbols, we
write AB // CD.
(Parallel lines are usually indicated by arrows.)
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Angle Sum Of Triangle(Book 1A p.239) Revision
The sum of the interior angles of any triangle is
180. i.e. In the figure, a b c
180. Reference ? sum of ?
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Angle Sum Of Triangle(Book 1A p.239) Revision
Example Calculate the unknown angles in the
following triangles.
(a)
(b)
(a) _______________ (b)
_______________
110
45
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Angle at a Point (P.131)
1. The two angles x and y have a common vertex
O, a common arm OB and lie on opposite sides of
the common arm OB. We say that x and y are a
pair of adjacent angles (??).
2. The sum of angles at a point is 360. e.g.
In the figure, a b c d 360. Reference
?s at a pt.
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Angle at a Point (P.131)

• Example 1

Find x in the figure.
x 210 90 360 (?s at a pt)
x 360 210 90
60
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Angle at a Point (P.131)

• Example 2

Find ?AOB in the figure.
2x 6x 240 360 (?s at a pt)
8x 120
x 15
? 2x 30
i.e. ?AOB 30
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Adjacent Angles on a Straight Line (P.133)
The sum of adjacent angles on a straight line is
180. e.g. In the figure, a b c 180.
Reference adj. ?s on st. line
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Adjacent Angles on a Straight Line (P.133)

• Example 1

In the figure, POQ is a straight line. Find q.
q 60 180 (adj. ?s on st. line)
q 180 60
120
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Adjacent Angles on a Straight Line (P.133)

• Example 2

In the figure, XOY is a straight line. Find ?.
30 90 ? 180 (adj. ?s on st. line)
? 180 30 90
60
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Adjacent Angles on a Straight Line (P.133)

• Example 3

In the figure, a light ray SP strikes a mirror HK
at pointP, and then reflects in the direction
PR. It is known that?SPH ?RPK. Suppose ?SPH
?, ?SPR ?. (a) Express ? in terms of ?. (b) If
? 32, find ?.
(a) ?RPK ?SPH ? Since HPK is a straight
line, ? ? ? 180 (adj. ?s on st. line) ?
? 180 2?
(b) When ? 32, ? 180 2 ? 32 116
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Adjacent Angles on a Straight Line (P.133)

• Example 4

In the figure, AOB is a straight line. (a) Find
?AOD. (b) If ?AOE 30, determine whether EOD
is a straight line.
(a) 3a 2a a 180 (adj. ?s on st. line)
6a 180
(b) ?EOD ?AOE ?AOD 30 150
180 ? EOD is a straight line.
a 30
?AOD 3a 2a
5a 5 ? 30 150
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Vertically Opposite Angles (P.137)
When two straight lines intersect, the vertically
opposite angles formed are equal. i.e. In the
figure, a b. Reference vert. opp. ?s
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Vertically Opposite Angles (P.137)

• Example 1

Find x and y in the figure.
x y
45 (vert. opp. ?s)
135 (vert. opp. ?s)
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Vertically Opposite Angles (P.137)

• Example 2

In the figure, the straight lines AE, BF and CG
intersect at O, and AE ? CG. Find p.
?BOA 75 (vert. opp. ?s) Consider all the
adjacent angles on the upper side of CG. ?COB
?BOA ?AOG 180 (adj. ?s on st. line) ?
p 75 90 180
p 15
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Vertically Opposite Angles (P.137)

• Example 3

In the figure, the straight lines PS and QT
intersect at R and ?TRS ?PQR. Find x and y.
In ?PQR, ?QPR ?PQR ?PRQ 180 (?
sum of ?) y 50 50 180
y 80
x 310 360 (?s at a pt) x
50 ? ?TRS ?PQR ?PRQ ?TRS
50 (Given)
50 (vert. opp. ?s)
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Time for Practice

• Pages 140 143 of Textbook 1B
• Questions 1 32
• Pages 54 57 of Workbook 1B
• Question 1 - 13

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Reminder

• Missing HW
• Detention
• Ch11 Ch 12 OBQ Correction
• 24 May (Fri)
• Ch 11 Ch 12 CBQ Correction and signature
• 24 May (Fri)
• Ch 10 SHW(I)
• 27 May (Mon)
• Ch 10 OBQ
• 29 May (Wed)

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• Enjoy the world of Mathematics!