Details of Class: Lesson 5 Date: Time: 100mins Learning Intentions/Topic: Year: 8 Geometry: Angles and Parallel lines Recognise parallel lines and calculate angles made by parallel lines and a transversal. Know and recognise the different types of angles that can be made by the transversal. Terms to know: Parallel Transversal Intersect Vertically Opposite Angles Corresponding Angles Co-Interior Angles Alternate Angles Resources Required: Room: No. of students: Relationship to VELS: Use angle relations involving transversals and pairs of parallel lines to solve problems, giving a reason for the solution Using language relevant to the topic Students to each have their own workbook and stationery Maths Quest 8 textbook Worksheets and Examples (provided) Whiteboard & Markers Ruler Introduction/Housekeeping/Warm-up: Link to last lesson : Previously we looked at calculating angles in triangles, quadrilaterals and other polygons. Now we will investigate different angles associated with parallel lines. 2 min Content Description: What are parallel lines? Parallel lines are lines that never meet. A line that intersects (crosses over) a pair (or set) of parallel lines is called a transversal. Draw this on the board labelling what are the parallel lines and what is the transversal. There are many angles that are made when a transversal crosses a set of parallel lines. Let’s look at the different types of angles that are made. Read through description as a class of the four different angles (p. 264 of Maths Quest 8) that are made when a transversal crosses parallel lines. - Vertically Opposite angles (X shape) - Corresponding angles (F shape) - Co-interior angles (C shape) - Alternate angles (Z shape) Activity: With the help of the information on p. 264, students are to complete the table provided. Resources Time 10 min Whiteboard & Markers, Ruler Maths Quest 8 p.264 Angles and Parallel lines table provided 7 min Quickly go through the answers to the table. Answer any questions that arise. 2 min Examples on board of how to find angles made by transversal and parallel lines. See sheet of examples provided. Example sheet 10 min Activity: Students to complete Ex 7G p.267 questions 2 - 14 Maths Quest 8 p.267 Remainder of Lesson Activity: When/if students finish Ex 7G, students are to complete: - Summary questions (fill in the blank) provided - Chapter review questions 1- 14 p. 287 – 289 Summary questions Maths Quest 8 pp.287 - 289 Reinforcement of Ideas/Questioning/Homework: Questions? Homework: Finish any unfinished questions from today’s activities. Overall reflection of lesson: 3 min Angles and Parallel lines Complete the table below. Keep completed table for your own reference. Diagram Type of angle relation Associated shape Rule X Corresponding Alternate Are equal in size Z Add up to 180°. Angles and Parallel lines Answers: Diagram Type of angle relation Associated shape Rule Vertically Opposite X Are equal Corresponding F Are equal in size Alternate Z Are equal Co-interior C Add up to 180° Examples: 1. For the diagram provided: a) State the type of angle relationship b) Find the value of the pronumeral 115˚ m a) The angles shown are co-interior b) m + 115˚ = 180˚ m = 180˚ – 115˚ m = 65˚ 2. Find the value of the pronumeral in the diagram shown. 85˚ x 85˚ y x y = 85˚ (as corresponding angles) x + y = 180˚ (as supplementary angles) x + 85˚ = 180˚ x = 180˚ - 85˚ = 95˚ Summary 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. An _____________ triangle has all 3 sides of equal length and all 3 angles equal. An isosceles triangle has _______________ of equal length and 2 base angles equal. All sides and all angles are different in ____________ triangles. An acute-angled triangle has all angles _________________ 90˚. An obtuse angled triangle contains one _____________angle. A ______________________triangle contains one 90˚ angle. The sum of the _______________ angles in any triangle is 180˚. An ________________________ of a triangle is equal to the sum of the two interior angles, not adjacent to it. All _________________________can be divided into 2 groups: parallelograms and others. Parallelograms have 2 pairs of_______________________ and include rectangles, squares, parallelograms and rhombi. A rectangle has two pairs of opposites sides equal and all four angles are ________ angles. A ______________has all 4 sides of equal length and four right-angles. A parallelogram has two pairs of ________________________ of equal length and opposite angles of equal size. A rhombus has __________________ sides of equal length and opposite angles of equal size. Other quadrilaterals include kites, _________________ and irregular quadrilaterals. The _______________________ of a kite are equal in length and the angles between the unequal sides are equal in size. A trapezium is a quadrilateral with _________________ of parallel sides. An _________________ quadrilateral does not have any special features. The sum of the interior angles in any quadrilateral is ___________. The sum of the interior angles is any polygon = 180˚ × (n – 2), where n is the _______________________ in the polygon. A _____________ polygon has all sides of equal length and all angles of equal size. A ______________is a line that intersects a pair (or set) of parallel lines. Corresponding angles (F-Shaped), ______________ angles (Z-shaped) and ____________________________ angles (X-shaped) are equal in size. Co-interior angles are _____________________ (that is, add to 180˚). Word List: 360˚ adjacent sides all four alternate equilateral exterior angle interior irregular number of sides obtuse one pair opposite sides parallel sides quadrilaterals regular right right-angled scalene smaller than square supplementary transversal trapeziums two sides verticallyopposite Summary | Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. An equilateral triangle has all 3 sides of equal length and all 3 angles equal. An isosceles triangle has two sides of equal length and 2 base angles equal. All sides and all angles are different in scalene triangles. An acute-angled triangle has all angles smaller than 90˚. An obtuse angled triangle contains one obtuse angle. A right-angled triangle contains one 90˚ angle. The sum of the interior angles in any triangle is 180˚. An exterior angle of a triangle is equal to the sum of the two interior angles, not adjacent to it. All quadrilaterals can be divided into 2 groups: parallelograms and others. Parallelograms have 2 pairs of parallel sides and include rectangles, squares, parallelograms and rhombi. A rectangle has two pairs of opposite sides equal and all four angles are right angles. A square has all 4 sides of equal length and four right-angles. A parallelogram has two pairs of opposite sides of equal length and opposite angles of equal size. A rhombus has all four sides of equal length and opposite angles of equal size. Other quadrilaterals include kites, trapeziums and irregular quadrilaterals. The adjacent sides of a kite are equal in length and the angles between the unequal sides are equal in size. A trapezium is a quadrilateral with one pair of parallel sides. An irregular quadrilateral does not have any special features. The sum of the interior angles in any quadrilateral is 360˚. The sum of the interior angles is any polygon = 180˚ × (n – 2), where n is the number of sides in the polygon. A regular polygon has all sides of equal length and all angles of equal size. A transversal is a line that intersects a pair (or set) of parallel lines. Corresponding angles (F-Shaped), alternate angles (Z-shaped) and vertically opposite angles (X-shaped) are equal in size. Co-interior angles are supplementary (that is, add to 180˚).