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Angles in Intersecting and Parallel Lines

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

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Angles in Intersecting and Parallel Lines

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

  2. Reminder • 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

  3. Reminder • 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)

  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 theunknown angles in thefollowing triangles. (a) (b) (a) _______________ (b) _______________ 110° 45°

  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° ∴2x = 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. In △PQR, QPR + PQR + PRQ = 180° (sum of ) y + 50° + 50° = 180° y = 80° x + 310° = 360° (s at a pt) x = 50° ∴ TRS = PQR PRQ = TRS = 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 1 - 13

  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 hare 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).

  14. Corresponding Angles (同位角)of Parallel Lines (P.147) The corresponding angles formed by parallel lines and atransversal 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 atransversal 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) Find x in the figure. • Example 1: x = 50° (corr. s, AB // CD)

  18. Angles formed by Parallel lines and a Transversal (P.146) Find x in the figure. • Example 2: 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) Find x in the figure. • Example 3: x + 45° = 180° (int. s, PQ // RS) ∴ x = 135°

  20. Angles formed by Parallel lines and a Transversal (P.146) Find a and b in the figure. • Example 4: 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

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