1. Angles in Intersecting and Parallel Lines
Form 1 Mathematics Chapter 10
Angles in Intersecting and Parallel Lines

2. Reminder Lesson requirement Before lessons start
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 Ch 11 & Ch 12 OBQ Correction
Detention
Ch 11 & Ch 12 OBQ Correction
24 May (Fri)
Ch 11 & Ch 12 CBQ Correction and signature

4. 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°)

5. 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

6. Relation between lines (Book 1A p.231-232) – Revision
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’.
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’.
(Parallel lines are usually indicated by arrows.)

7. 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 ]

8. Angle Sum Of Triangle (Book 1A p.239) – Revision
Example: Calculate the unknown angles in the following triangles.
(a)
(b)
(a) _______________ (b) _______________
45°
110°

9. 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 (鄰角).
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.]

10. 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°

11. 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°
∴ x = 30°
i.e AOB = 30°

12. 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]

13. 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°

14. 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°

15. Adjacent Angles on a Straight Line (P.133)
Example 3:
In the figure, a light ray SP strikes a mirror HK at point P, 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°

16. 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°

17. 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]

18. Vertically Opposite Angles (P.137)
Example 1:
Find x and y in the figure. x y
= 45° (vert. opp. s)
= 135° (vert. opp. s)

19. 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°

20. 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.
x + 310° = 360° (s at a pt)
x = 50°
∴ TRS = PQR
PRQ = TRS
In △PQR,
QPR + PQR + PRQ = 180°
( sum of )
y + 50° + 50° = 180°
y = 80°
= 50° (Given)
= 50° (vert. opp. s)

21. Time for Practice Pages 140 – 143 of Textbook 1B
Questions 1 – 32
Pages 54 – 57 of Workbook 1B
Question

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

23. Enjoy the world of Mathematics!
Ronald HUI