Starter Questions B 6 co A C 8 34o General

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

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

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 www.mathsrevision.com 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

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

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

Begin Maths in Action Worksheet 1 Isosceles triangles in Circles General Begin Maths in Action Worksheet 1 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

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

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 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

Isosceles triangles in Circles 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 www.mathsrevision.com A B The angle in a semi-circle is ALWAYS 90o Sunday, 09 December 2018 Created by Mr Lafferty

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. www.mathsrevision.com Remember - Angles in any triangle sum to 180o Sunday, 09 December 2018 Created by Mr Lafferty

Finish Maths in Action Worksheet 2 Angles in a Semi-Circle General Finish Maths in Action Worksheet 2 Then Page 114 Ex3 Q3,Q4,Q5 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

Starter Questions www.mathsrevision.com x xo 4 z y 3 56o General Sunday, 09 December 2018 Created by Mr Lafferty

Solve harder semi-circle problems Angles in a Semi-Circle General Aim of Today’s Lesson Solve harder semi-circle problems www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

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

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 www.mathsrevision.com 60o E 25o A B Sunday, 09 December 2018 Created by Mr Lafferty

Angles in a Semi-Circle General Page 114 Ex4 Q1 – Q3 Then Worksheet 3 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

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

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 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

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 www.mathsrevision.com Sunday, 09 December 2018 Created by Mr Lafferty

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

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