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Circles Isosceles triangles in a circle Angles in a semi-circle

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Presentation on theme: "Circles Isosceles triangles in a circle Angles in a semi-circle"— Presentation transcript:

1 Circles Isosceles triangles in a circle Angles in a semi-circle
General Isosceles triangles in a circle Angles in a semi-circle Pythagoras Theorem SOHCAHTOA Tangent line on a circle Sunday, 09 December 2018 Created by Mr Lafferty

2 Starter Questions www.mathsrevision.com B 6 co A C 8 34o General
Sunday, 09 December 2018 Created by Mr Lafferty

3 To identify isosceles triangles
Isosceles triangles in Circles General Aim of Today’s Lesson To identify isosceles triangles within a circle. Sunday, 09 December 2018 Created by Mr Lafferty

4 Isosceles triangles in Circles
General When a line is drawn between two points on a circle it is called a CHORD. If the line passes through the Centre it is called a diameter. A B xo xo When two radii are drawn to the ends of a chord, an isosceles triangle is formed. C Sunday, 09 December 2018 Created by Mr Lafferty

5 Isosceles triangles in Circles
General Special Properties of Isosceles Triangles Two equal lengths Two equal angles Angles in any triangle sum to 180o Sunday, 09 December 2018 Created by Mr Lafferty

6 Isosceles triangles in Circles
General Q. Find the angle xo. Solution Angle at C is equal to: B xo C Since the triangle is isosceles we have A 280o Sunday, 09 December 2018 Created by Mr Lafferty

7 Begin Maths in Action Worksheet 1 or Ex 2
Isosceles triangles in Circles General Begin Maths in Action Worksheet 1 or Ex 2 Sunday, 09 December 2018 Created by Mr Lafferty

8 Starter Questions www.mathsrevision.com B bo 5 A C 12 27o General
Sunday, 09 December 2018 Created by Mr Lafferty

9 To find the special angle
Angles in a Semi-Circle General Aim of Today’s Lesson To find the special angle in a semi-circle Sunday, 09 December 2018 Created by Mr Lafferty

10 Angles in a Semi-Circle
General On your worksheet, mark the point P on the circumference of the semicircle. Joint the points AP and BP together. Measure angle ∠APB P A B The angle in a semi-circle is ALWAYS 90o Sunday, 09 December 2018 Created by Mr Lafferty

11 Angles in a Semi-Circle
General KeyPoint for Angles in a Semi-circle P A B A triangle APB inscribed within a semicircle with hypotenuse equal to the diameter will ALWAYS be right angled at P on the circumference. Remember - Angles in any triangle sum to 180o Sunday, 09 December 2018 Created by Mr Lafferty

12 Angles in a Semi-Circle
General Example 1 : Sketch diagram and find all the missing angles. 20o Hints 43o Look for right angle triangles Remember ! Angles in any triangle sum to 180o 47o 70o Sunday, 09 December 2018 Created by Mr Lafferty

13 Angles in a Semi-Circle
General Example 2 : Sketch the diagram. (a) Right down two right angle triangles (a) Calculate all missing angles. D C 60o E 25o A B Sunday, 09 December 2018 Created by Mr Lafferty

14 Finish Maths in Action Worksheet 2 Then Page 114 Ex3 and Ex4
Angles in a Semi-Circle General Finish Maths in Action Worksheet 2 Then Page 114 Ex3 and Ex4 Sunday, 09 December 2018 Created by Mr Lafferty

15 Starter Questions www.mathsrevision.com General
Sunday, 09 December 2018 Created by Mr Lafferty

16 Angles in a Semi-Circle
General Pythagoras Theorem Aim of Today’s Lesson How we can use Pythagoras Theorem to calculate length within a circle Sunday, 09 December 2018 Created by Mr Lafferty

17 Angles in a Semi-Circle
General Pythagoras Theorem We have been interested in right angled triangles within a semi-circle. Since they are right angled we can use Pythagoras Theorem to calculate lengths. Example 1 : Calculate the value of d P A B 4cm 3cm d cm Sunday, 09 December 2018 Created by Mr Lafferty

18 Angles in a Semi-Circle
General Pythagoras Theorem Example 2 : Calculate the length of XY Y 12cm cm X Z 13 cm Sunday, 09 December 2018 Created by Mr Lafferty

19 MIA Page 116 Ex5 Angles in a Semi-Circle www.mathsrevision.com
General Pythagoras Theorem MIA Page 116 Ex5 Sunday, 09 December 2018 Created by Mr Lafferty

20 Starter Questions www.mathsrevision.com General
Sunday, 09 December 2018 Created by Mr Lafferty

21 Angles in a Semi-Circle
General SOHCAHTOA Aim of Today’s Lesson How we can use SOHCAHTOA to calculate length and angles within a circle Sunday, 09 December 2018 Created by Mr Lafferty

22 Angles in a Semi-Circle
General SOHCAHTOA We have been interested in right angled triangles within a semi-circle. Since they are right angled we can use SOHCAHTOA to calculate lengths and angles. Example 1 : Calculate the value of angle xo P A B 4cm 3cm d cm xo Sunday, 09 December 2018 Created by Mr Lafferty

23 Angles in a Semi-Circle
General SOHCAHTOA Example 2 : Calculate the length of AB B 67.4o A C 13 cm Sunday, 09 December 2018 Created by Mr Lafferty

24 Maths In Action Page 117 Ex6 Angles in a Semi-Circle
General SOHCAHTOA Maths In Action Page 117 Ex6 Sunday, 09 December 2018 Created by Mr Lafferty

25 Starter Questions www.mathsrevision.com General
Sunday, 09 December 2018 Created by Mr Lafferty

26 Tangent to the circle Aim of Today’s Lesson
General Aim of Today’s Lesson To understand what a tangent line is and its special property with radius at the point of contact. Sunday, 09 December 2018 Created by Mr Lafferty

27 Tangent to the circle www.mathsrevision.com
General A tangent line is a line that touches a circle at only one point. Sunday, 09 December 2018 Created by Mr Lafferty

28 Tangent to the circle www.mathsrevision.com
General A tangent line is a line that touches a circle at only one point. Which of the lines are tangent to the circle? Sunday, 09 December 2018 Created by Mr Lafferty

29 Tangent to the circle www.mathsrevision.com
General The radius of the circle that touches the tangent line is called the point of contact radius. Special Property The point of contact radius is always perpendicular (right-angled) to the tangent line. Sunday, 09 December 2018 Created by Mr Lafferty

30 Tangent to the circle www.mathsrevision.com
General Q. Find the length of the tangent line between A and B. Solution Right-angled at A since AC is the radius at the point of contact with the Tangent. B 10 By Pythagoras Theorem we have A C 8 Sunday, 09 December 2018 Created by Mr Lafferty

31 Begin Maths in Action Book
Tangent to the circle General Begin Maths in Action Book Ex7A & Ex7B page 185 Sunday, 09 December 2018 Created by Mr Lafferty

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