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 10 SHW(I) Ch 10 SHW(II) Ch 10 SHW(III)
Detention
Ch 10 SHW(I)
28 May (Tue)
Ch 10 SHW(II)
31 May (Fri)
Ch 10 SHW(III)
Ch 10 OBQ
Ch 10 CBQ
4 June (Tue)

4. 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 ]

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

6. Angle at a Point (P.131) The sum of angles at a point is 360°.
e.g. In the figure, a + b + c + d = 360°.
[Reference: s at a pt.]

7. 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°

8. 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]

9. 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°

10. 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]

11. 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)

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

13. Angles formed by Two lines and a Transversal (P.145)
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 pairs of 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).

14. Corresponding Angles (同位角) of Parallel Lines (P.147)
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]

15. Alternate Angles (內錯角) of Parallel Lines (P.148)
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]

16. Interior Angles (同旁內角) on Same side of Transversal (P.149)
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]

17. Angles formed by Parallel lines and a Transversal (P.146)
Example 1:
Find x in the figure.
x = 50° (corr. s, AB // CD)

18. Angles formed by Parallel lines and a Transversal (P.146)
Example 2:
Find x in the figure.
x = 135° (alt. s, AB // CD)
OR x + 45° = 180° (int. s, AB // CD)
x = 135°

19. Angles formed by Parallel lines and a Transversal (P.146)
Example 3:
Find x in the figure.
x + 45° = 180° (int. s, PQ // RS)
∴ x = 135°

20. Angles formed by Parallel lines and a Transversal (P.146)
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°

21. Angles formed by Parallel lines and a Transversal (P.146)
Find x and y in the figure.
Example 5:
x + 30° + 50° = 180°
( sum of )
x = 100°
y = x (alt. s, AB // CE)
∴ y = 100°

22. Angles formed by Parallel lines and a Transversal (P.146)
Example 6:
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° r q p

23. Angles formed by Parallel lines and a Transversal (P.146)
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° y A

24. Time for Practice Pages 154 – 155 of Textbook 1B
Questions 4 – 25
Pages 59 – 61 of Workbook 1B
Question 1 - 8

25. Enjoy the world of Mathematics!
Ronald HUI