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

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

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

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°)

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

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.)

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 ]

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

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.]

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°

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°

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]

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°

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°

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°

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°

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]

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

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°

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)

Time for Practice Pages 140 – 143 of Textbook 1B Questions 1 – 32 Pages 54 – 57 of Workbook 1B Question 1 - 13

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)

Enjoy the world of Mathematics! Ronald HUI