Form 1 Mathematics Chapter 10

 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

 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)

The sum of the interior angles of any triangle is 180°. i.e.In the figure, a + b + c = 180 °. [Reference:  sum of  ]

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

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]

When two straight lines intersect, the vertically opposite angles formed are equal. i.e. In the figure, a = b. [Reference: vert. opp.  s]

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]

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]

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]

 Example 6: p q 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°

 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 ° = 180° (int.  s, PQ // AT) ∴ y = 35° 67° + x + y = 180° (int.  s, NS // AT) 67° + x + 35° = 180° x = 78° A y

 Pages 154 – 155 of Textbook 1B  Questions 4 – 25  Pages 59 – 61 of Workbook 1B  Question 1 - 8

The conditions needed for two lines to be parallel: 1. If the corresponding angles formed by two lines and a transversal are equal, then the two lines are parallel. i.e.In the figure, if a = b, then AB // CD. [Reference: corr.  s equal]

The conditions needed for two lines to be parallel: 2. If two lines are cut by a transversal and the alternate angles are equal, then the two lines are parallel. i.e.In the figure, if a = b, then AB // CD. [Reference: alt.  s equal]

The conditions needed for two lines to be parallel: 3. If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, then the two lines are parallel. i.e.In the figure, if a + b = 180°, then AB // CD. [Reference: int.  s supp.]

 Example 1: Are the lines AB and CD in the figure parallel to each other? ∵  BFG =  DGH = 75 ° ∴ AB // CD ( corr.  s equal )

 Example 2: Determine if lines AC and DF as shown in the figure are parallel. ∵  ABE =  FEB = 125 ° ∴ AC // DF (alt.  s equal)

 Example 3: Determine if lines AB and DC as shown in the figure are parallel. ∵  ABC +  DCB ∴ AB // DC (int.  s supp.) = 150° + 30° = 180°

 Example 4: Determine if lines DE and FG as shown in the figure are parallel.  FCB + 35° + 50° = 180° (adj.  s on st. line) ∴  FCB = 180° – 35° – 50° = 95° ∵  DBA =  FCB = 95° ∴ DE // FG (corr.  s equal)

 Example 5: In the figure, AB // CD,  ABC = 40 °,  BCD = 2p,  CDE = 3p – 20°. (a) Find p. (b) Is it true that BC // DE? Give reasons. (a) 2p = 40° (alt.  s, AB // CD) p = 20° (b)  BCD = 2p = 40°  CDE = 3p – 20° = 3  20° – 20° = 40° ∵  BCD =  CDE = 40° ∴ BC // DE (alt. ∠ s equal)

 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)

Enjoy the world of Mathematics! Ronald HUI