Ch. 4 Angles and Parallel Lines Math 10-3. Day 1: Angles and Parallel Lines.
Angles in Intersecting and Parallel Lines
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Form 1 Mathematics Chapter 10
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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
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Missing HW Detention
Ch 10 SHW(I) 28 May (Tue)
Ch 10 SHW(II) 31 May (Fri)
Ch 10 SHW(III) 31 May (Fri)
Ch 10 OBQ 31 May (Fri)
Ch 10 CBQ 4 June (Tue)
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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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Example: Calculate the unknown angles in the following triangles.
(a)
(a) _______________ (b) _______________45° 110°
(b)
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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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Example 2:
i.e. AOB = 30°
Find AOB in the figure.
2x + 6x + 240° = 360° (s at a pt)
8x = 120°
x = 15°
∴ 2x = 30°
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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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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)
(b) EOD
= AOE + AOD
= 30° + 150°
= 180°
∴ EOD is a straight line.
6a = 180°
a = 30°
AOD = 3a + 2a
= 5a = 5 30°
= 150°
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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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Example 3:
In the figure, the straight
lines PS and QT intersect
at R and TRS = PQR.
Find x and y.
x + 310° = 360° (s at a pt)
x = 50°
∴ TRS = PQR
PRQ = TRS
= 50° (Given)
= 50° (vert. opp. s)
In △PQR,
QPR + PQR + PRQ = 180°
( sum of )
y + 50° + 50° = 180°
y = 80°
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Pages 140 – 143 of Textbook 1B Questions 1 – 32
Pages 54 – 57 of Workbook 1B Question 1 - 13
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According to the figure,
1. the straight line EF is called the transversal (截線 ) of AB and CD.
2. a and e, b and f, c and g, d and h are pairsof corresponding angles (同位角 ).
3. c and e, d and f are pairs of alternate angles (內錯角 ).
4. c and f, d and e are pairs of interior angles on the same side of the transversal (同旁內角 ).
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The corresponding angles formed by parallel lines and a
transversal are equal.
i.e. In the figure, if AB // CD, then a = b.
[Reference: corr. s, AB // CD]
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The alternate angles formed by parallel lines and a
transversal are equal.
i.e. In the figure, if AB // CD, then a = b.
[Reference: alt. s, AB // CD]
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The sum of the interior angles of parallel lines on the
same side of the transversal is 180°.
i.e. In the figure, if AB // CD, then a + b = 180°.
[Reference: int. s, AB // CD]
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Example 1: Find x in the figure.
x = 50° (corr. s, AB // CD)
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Example 2: Find x in the figure.
x = 135° (alt. s, AB // CD)
OR x + 45° = 180° (int. s, AB // CD) x = 135°
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Example 3: Find x in the figure.
∴ x = 135°
x + 45° = 180° (int. s, PQ // RS)
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Example 4:Find a and b in the figure.
a + 120° = 180° (int. s, AD // BE)
a = 60°
EBC = DAC (corr. s, AD // BE)
b + 50° = 120°
b = 70°
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Example 5:Find x and y in the figure.
x + 30° + 50° = 180° ( sum of )
x = 100°
y = x (alt. s, AB // CE)
∴ y = 100°
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Example 6:
pq
r
In the figure, AB, QR and CD are parallel
lines, while PQ and RS are another pair of
parallel lines. If RSA = 66°, find QPD.
Using the notation in the figure,r + 66° = 180° (int. s, AD // QR) r = 114°∵ q = r (alt. s, PQ // RS)
∴ q = 114° ∵ p + q = 180° (int. s, QR // CD)
p + 114° = 180° p = 66°
∴ QPD = 66°
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Example 7:Find the unknown angle x in the figure.
Draw the straight line AT such that AT // PQ.Since PQ // NS, we have AT // NS.Using the notation in the figure,
y + 145° = 180° (int. s, PQ // AT)
∴ y = 35° 67° + x + y = 180° (int. s, NS // AT)
67° + x + 35° = 180°
x = 78°
Ay
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Pages 154 – 155 of Textbook 1B Questions 4 – 25
Pages 59 – 61 of Workbook 1B Question 1 - 8
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Enjoy the world of Mathematics!
Ronald HUI