S3_General_Chapter2_TJ_Angles

S3_General_Chapter2_TJ_Angles - Angles G e ne ra l Revising...

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Unformatted text preview: Angles G e ne ra l Revising Basic Angles Naming Angles Measuring Angles Finding Missing angles Drawing Triangles Angles in a Triangle Corresponding Angles Alternate Angles Angles in a Quadrilateral Feb 13, 2012 Created by Mr.Lafferty Math Dept www.mathsrevision.com Starter Questions General Q1. Convert to the 24 hour clock. (a) 7:25 pm (b) 6:50 am www.mathsrevision.com Q2. Q3. Q4. (a) Feb 13, 2012 Write down the type of angle that is less than 90 deg. Calculate 2.34 + 4.7 + 0.12 Round the following to nearest 1000. 12,501 (b) 369,765 Created by Mr.Lafferty Math Dept Type of Angles General Learning Intention Success Criteria 1. To be able to identify acute, rightangle, obtuse, straight line and reflex angles. www.mathsrevision.com 1. To revise Type of Angles. Feb 13, 2012 Created by Mr.Lafferty Math Dept Type of Angles G e ne ra l Vertical www.mathsrevision.com Acute less than 90o Horizontal Right Angle exactly 90o Obtuse Between 90o 180o Straight Line Angle exactly 180o Feb 13, 2012 Created by Mr.Lafferty Math Dept reflex over 180o less than 360o Type of Angles G e ne ra l www.mathsrevision.com Now try Ch2 (page 14) Exercise 1 Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions General Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40 www.mathsrevision.com Q2. Q3. Q4. (a) Feb 13, 2012 Write down 2 numbers that add to give 8 and multiply to give 15. Calculate 5.65 1.3 Round the following to nearest 100. 13,551 (b) 369,449 Created by Mr.Lafferty Math Dept Naming Angles General Learning Intention Success Criteria 1. To be able to name an angle. 2. Understand the difference between the type of angle and the name of an angle. www.mathsrevision.com 1. To explain how we name angles by THREE capital letters with the angle sign. The middle letter being where the angle is. Feb 13, 2012 Created by Mr.Lafferty Math Dept Naming Angles General A X www.mathsrevision.com B C Type of angle is acute Name of angle is ABC Z Y Type of angle is obtuse Name of angle is ZYX MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS ALWAYS 3 CAPITAL LETTERS Feb 13, 2012 Created by Mr.Lafferty Math Dept Naming Angles G e ne ra l www.mathsrevision.com Now try Ch2 (page 15) Exercise 2 Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40 Q2. Q3. Q4. (a) Write down lowest common multiple of 3, 4 , 5. List the prime numbers between 10 and 20. Round the following to nearest 100. 13,551 (b) 369,449 13 Feb 2012 Created by Mr. Lafferty 10 A 180o Protractor Outside scale from 0o to 180o going in a clockwise direction. 13 Feb 2012 Inside scale from 0o to 180o going in an anticlockwise direction. 11 You need to be able to measure an angle to the nearest degree. To help you do this you should always: 1. Look directly down onto the cross point. 2. Always use the protractor in a horizontal manner as shown below. 13 Feb 2012 12 Measuring Angles with a 180o Protractor 50o 2 67o 1 0 on the inside so use inside scale 13 Feb 2012 0 on the outside so use outside scale 13 Measuring Angles with a 180o Protractor 3 120o 4 135o 0 on the inside so use inside scale 13 Feb 2012 0 on the outside so use outside scale 14 Naming Angles General www.mathsrevision.com Now try Ch2 (page 17) Exercise 3 Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions General 1. Calculat e: www.mathsrevision.com ( a ) 6 7 ( b ) 10 + ( 3 ) ( c ) 2 12 Q 2 . Co nve r t t o 12 h r s c lo c k ( a) 2 3 0 0 h r s ( b ) 14 2 3 h r s Q .3 S o lve 5 x 4 5 = 7 0 Feb 13, 2012 Created by Mr.Lafferty Math Dept Find Missing Angles General Learning Intention Success Criteria 1. To know 360o in a circle. 2. Find missing angle given all other angles. www.mathsrevision.com 1. To calculate missing angle give all other angles. Feb 13, 2012 Created by Mr.Lafferty Math Dept Find Missing Angle General 55o www.mathsrevision.com 35 Two angles making a o right angle add up to 90 (Complementary angles) o 115o 65 o Two angles making a o straight line add up to 180 (Supplementary angles) 146o 34 o Angles opposite each other at a cross are equal. Feb 13, 2012 146o 34 o 120 o Angles round a point o always add up to 360 Created by Mr.Lafferty Math Dept 145o 95 o Angles and Triangles General 1 2 Angle x = 180 47 = 133 o www.mathrevision.com y 114o Angle y = 180 114 = 66o 47 o x 3 Angle a = 180 76 = 104o 4 Angle b = 180 82 = 98o Created by Mr Lafferty a 76 Monday 13 February 2012 82o b o 19 Angles and Triangles General Example www.mathsrevision.com Find angle x. x o 105 100 o Think ! 360o o Angle x = 360 (90 + 100 + 105 ) = 360 295 = 65 Monday 13 February 2012 o o o o o + o o o 90 100 105 295 20 Created by Mr Lafferty Find Missing Angle General www.mathsrevision.com Now try Ch2 (page 20) Exercise 4 Feb 13, 2012 Created by Mr.Lafferty Math Dept (SAS) Starter Questions Q1. (a) Convert the percentages to fractions. 30% (b) 60% 80 o Q2. Q3. Q4. (a) 13 Feb 2012 Write down all the factors of 16. Calculate the missing angles. Round the following to 1 decimal place. 4.549 (b) 6.551 22 Created by Mr. Lafferty Drawing SAS Triangles SAS Triangles Side Angle Side 13 Feb 2012 Created by Mr. Lafferty 23 Drawing SAS Triangles Toolkit required 1. Ruler 2. Protractor 3. Pencil & Paper 13 Feb 2012 Created by Mr. Lafferty 24 Drawing SAS Triangles C A Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30o and AC = 5cm 30 o B Step 1 Draw line AB=6cm Step 2 Measure angle CAB from A C X Step 3 Draw the line AC = 5cm through X. Label it C. Step 4 Join C to B. A B Check angles add to 180o 13 Feb 2012 Created by Mr. Lafferty 25 Find Missing Angle General www.mathsrevision.com Now try Ch2 (page 22) Exercise 5 Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions General 1. Solve t he equat ion 5x- 3 =18 (decimal value) Calculat e (- 13) + (- 1)- 15 Calculat e x: Change 790cm int o m What is t he coordinat e C(- 8,- 4) ref lect ed in t he x- axis? x o www.mathsrevision.com 2. 3. 4. 5. 75 o Feb 13, 2012 Created by Mr.Lafferty Math Dept Sum of Angles in a Triangle General Learning Intention Success Criteria 1. To know all angles in a triangle o add to 180 . 2. Use knowledge to solve problems. www.mathsrevision.com 1. To show that all the angles o in a triangle sum to 180 . Feb 13, 2012 Created by Mr.Lafferty Math Dept To determine the General angle sum of any Triangle Cut off corners www.mathsrevision.com Cut off corners Cut off corners Feb 13, 2012 Created by Mr.Lafferty Math Dept angle sum of any Triangle General www.mathsrevision.com All angles in a triangle ALWAYS o added up to180 180 Feb 13, 2012 o Created by Mr.Lafferty Math Dept Angles and Triangles General www.mathsrevision.com Equilateral Triangle 3 equal sides 3 equal angles. Monday 13 February 2012 Isosceles triangle 2 equal sides 2 equal angles (base) Created by Mr Lafferty Rightangled triangle One angle is 90 o 31 Angles and Triangles General Example 1 Calculate angle a. 65o a www.mathsrevision.com An g le a = 1 8 0 (9 0 + 6 5 ) = 1 8 0 1 5 5 = 2 5 o Example 2 Calculate angles a, b and c Since the triangle is equilateral, angles a, b and c are all 60o (180/3) Monday 13 February 2012 Created by Mr Lafferty b a c 32 Angles and Triangles General Example 3 b Angle a = 65o (base angles of an isosceles triangle are equal). Angle b = 180 (65 + 65) = 180 130 = 50o www.mathsrevision.com Calculate angle a. 65o Example 4 Calculate angles x and y A ng le s x and y = Monday 13 February 2012 a 130o x y 18 0 13 0 2 50 = =25o 2 Created by Mr Lafferty 33 Angles and Triangles General Example 5 www.mathsrevision.com Calculate angles a and b. Isosceles triangle a b 18 0 9 0 A ng le s a and b = 2 90 = = 45o 2 Monday 13 February 2012 Created by Mr Lafferty 34 Sum of Angles in a Triangle General Copy out the following triangles and find the missing angles. www.mathsrevision.com x 87 o o 50 o 38 o 32 o x o x o x o Remember all the angles add up to 180 Feb 13, 2012 Created by Mr.Lafferty Math Dept o Sum of Angles in a Triangle G e ne ra l www.mathsrevision.com Now try Ex 6 Ch2 (page 23) Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions General Q1. Solve the equation below www.mathsrevision.com Q2. Find two numbers that multiply to give 18 and subtract to give 3. Find the average and range of the numbers below 2,8,8,10 2 x + 16 = 2 8 Q3. Q4. Find 6 0 % o f 2 4 0 Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Learning Intention Corresponding Angles Success Criteria 1. To understand the term corresponding angles. 2. To be able to use property to solve problems. www.mathsrevision.com 1. To explain the term corresponding angles and show how we use the property to solve problems. Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles G e ne ra l Corresponding Angles www.mathsrevision.com Which angles are equal? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles G e ne ra l Corresponding Angles www.mathsrevision.com Which angles are equal? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles G e ne ra l Corresponding Angles Which angles are equal to the shaded angle? www.mathsrevision.com Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles G e ne ra l www.mathsrevision.com Which angles are equal to the shaded angle? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles www.mathsrevision.com look for shapes Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles What is the value of letter x? www.mathsrevision.com 120 120 x Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles www.mathsrevision.com 100 What is the value of letter a? 100 a Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles b 48 www.mathsrevision.com 48 What is the value of letter b? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles What is the value of letter c? www.mathsrevision.com 110 110 c Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General 70 70 Corresponding Angles www.mathsrevision.com b10 1 a What are the values of letters a and b? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles www.mathsrevision.com 115 115 65 What are the values of the missing angles? Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles What are the values of the missing angles? 123 123 57 57 www.mathsrevision.com Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Corresponding Angles www.mathsrevision.com Now try Ch2 Extension Booklet Ex7E Page 1 Q1 to Q4 Feb 13, 2012 Created by Mr.Lafferty Math Dept General Starter Questions Q1. Solve the equation below Find two numbers that multiply to give 48 and divide to give 3. Find missing angles 119o ao bo www.mathsrevision.com Q2. 4x -7 = 9 Q3. Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Learning Intention Alternate Angles Success Criteria 1. To understand the term alternate angles. 2. To be able to use property to solve problems. www.mathsrevision.com 1. To explain the term alternate angles and show how we use the property to solve problems. Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles www.mathsrevision.com Look for Z shapes = equal angles Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles Find the value of a ? www.mathsrevision.com 35 35 a Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles b 43 www.mathsrevision.com Find the value of b ? 43 Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles Find the value of c ? www.mathsrevision.com 33 33 c Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles 123 www.mathsrevision.com Find the value of d ? 123 d Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles 50 www.mathsrevision.com Find the value a and b ? 130 b a 50 Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles www.mathsrevision.com 135 c 45 Find the value of a and b ? 45 d Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles 60 1 c20 www.mathsrevision.com Find the value a, b and c ? 120 b 60 a Feb 13, 2012 Created by Mr.Lafferty Math Dept Angles General Alternate Angles www.mathsrevision.com Now try Ch2 Extension Booklet Ex7E Page 4 Q5 to Q7 Feb 13, 2012 Created by Mr.Lafferty Math Dept Starter Questions General Q1. List 4 properties of a square. Simplify the following fraction 35 10 0 www.mathsrevision.com Q2. Q3. Q4. ( a ) 2 5 % ( b ) 12 .5 % Solve Express the following percentages as fractions 2x + 4 = 22 Created by Mr.Lafferty Monday 13 February 2012 63 Angles in a Quadrilateral General IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360 o www.mathsrevision.com B b o c VA BC and VA CD o C a o +b o +c o +d o = 360o We have split the quadrilateral into two triangles But for any triangle 0 the sum of the angles is 180 o o A a o d o D Hence for the quadrilateral we have 2 x 180 =360 Monday 13 February 2012 Angles in a Quadrilateral General Question : Find the missing angle below. www.mathsrevision.com The four angles of a quadrilateral add to = 360 o w z o 34 100 yo o x 9 0 o + 3 4 o + 10 0 o + y o = 3 6 0 o y o = 360o -224o y o = 13 6 o Created by Mr.Lafferty y Monday 13 February 2012 65 General Angles in a Quadrilateral Angles www.mathsrevision.com Now try Ch2 Extension Booklet Ex8E Page 7 Feb 13, 2012 Created by Mr.Lafferty Math Dept ...
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