Pythagoras Theorem National 4 REL 1 2 a

Pythagoras Theorem National 4 REL 1. 2 a www. mathsrevision. com Squaring a Number and Square Roots Investigating Pythagoras Theorem Calculating the Hypotenuse Solving real-life problems Finding the length of the smaller side Distance between two points Mixed problems 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Squaring a Number www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. To understand the term ‘squaring a number’. 1. To understand what is meant by the term ‘squaring a number’ 2. Be able to calculate squares both mentally and using the calculator. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Squaring a Number National 4 REL 1. 2 a www. mathsrevision. com To square a number means to : “Multiply it by itself” Example : means 9 x 9 = 81 means 10 x 10 = 100 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Squaring a Number www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 1 Ch 13 (page 151) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Square Root of a number National 4 REL 1. 2 a www. mathsrevision. com You now know how to find : 92 = 9 x 9 = 81 We can ‘undo’ this by asking “which number, times itself, gives 81” From the top line, the answer is 9 This is expressed as : “the SQUARE ROOT of 81 is 9” or in symbols we write : 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Square Root of a Number www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 2 Ch 13 (page 153) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a Starter Questions 115 o Q 1. Are the missing angles 65 o, 40 o and 65 o Q 2. Calculate Q 3. The cost of a new computer is £ 1000 +vat. If the vat is charged at 12% what is the total cost. Q 4. The cost of a bag of sugar is £ 1. 12. How much 50 bags cost. 30 -Nov-20 NON-CALCULATOR Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a Right – Angle Triangles Aim of today's Lesson ‘To investigate the right-angle triangle and to come up with a relationship between the lengths of its two shorter sides and the longest side which is called the hypotenuse. ‘ 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Right – Angle Triangles a? 3 What is the length of b ? 4 What is the length of Copy the triangle into your jotter and measure the length of c 5 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 a ? 6 What is the length of b ? 8 What is the length of Copy the triangle into your jotter and measure the length of c 10 Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Right – Angle Triangles What is the length of a? 5 What is the length of b ? 12 Copy the triangle into your jotter and measure the length of c 13 Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a Right – Angle Triangles Copy the table below and fill in the values that are missing a b c 3 4 5 5 12 13 6 8 10 30 -Nov-20 a 2 b 2 Compiled by Mr. Lafferty Maths Dept. c 2

Right – Angle Triangles www. mathsrevision. com National 4 REL 1. 2 a a b c a 2 b 2 c 2 3 4 5 9 16 25 5 12 13 25 144 169 6 8 10 36 64 100 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept. Can anyone spot a relationship between a 2, b 2, c 2.

www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Pythagoras’s Theorem c b a Compiled by Mr. Lafferty Maths Dept.

www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Summary of Pythagoras’s Theorem Note: The equation is ONLY valid for right-angled triangles. Compiled by Mr. Lafferty Maths Dept.

Pythagoras Theorem www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 3 Ch 13 (page 154) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Calculating Hypotenuse www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. Use Pythagoras Theorem to calculate the length of the hypotenuse “the longest side” 30 -Nov-20 1. Know the term hypotenuse “ the longest side” 2. Use Pythagoras Theorem to calculate the hypotenuse. Compiled by Mr. Lafferty Maths Dept.

Calculating the Hypotenuse www. mathsrevision. com National 4 REL 1. 2 a Example 1 Q 2. 30 -Nov-20 Calculate the longest length of the rightangled triangle below. c 8 12 Compiled by Mr. Lafferty Maths Dept.

Calculating the Hypotenuse www. mathsrevision. com National 4 REL 1. 2 a Example 2 Q 1. An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present which is 15 km from the airport. It is at a height of 8 km. 30 -Nov-20 How far away is the plane from the airport? Aeroplane c Airport Compiled by Mr. Lafferty Maths Dept. b=8 a = 15 Lennoxtown

Calculating Hypotenuse www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 4 Ch 13 (page 156) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. To show Pythagoras Theorem can be used to solve real-life problems. 30 -Nov-20 1. Solve real-life problems using Pythagoras Theorem. Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems www. mathsrevision. com National 4 REL 1. 2 a When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length. Example : A steel rod is used to support a tree which is in danger of falling down. What is the length of the rod? rod 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept. 8 m 15 m

Solving Real-Life Problems www. mathsrevision. com National 4 REL 1. 2 a Example 2 A garden is rectangular in shape. A fence is to be put along the diagonal as shown below. What is the length of the fence. 10 m 15 m 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 5 Ch 13 (page 159) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. To show Pythagoras Theorem can be used to find the length of the smaller side. 30 -Nov-20 1. Use Pythagoras Theorem to find the length of smaller side. Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side www. mathsrevision. com National 4 REL 1. 2 a To find the length of the smaller side of a right- angled triangle we simply rearrange Pythagoras Theorem. Example : Find the length of side a ? Check answer ! Always smaller than hypotenuse 30 -Nov-20 20 cm a cm Compiled by Mr. Lafferty Maths Dept. 12 cm

Length of the smaller side www. mathsrevision. com National 4 REL 1. 2 a Example : Find the length of side b ? 10 cm Check answer ! Always smaller than hypotenuse 30 -Nov-20 8 cm Compiled by Mr. Lafferty Maths Dept. b cm

Length of smaller side www. mathsrevision. com National 4 REL 1. 2 a Now try Exercise 6 Ch 13 (page 161) 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a ALWAYS comes up in exam !!

Finding the Length of a Line www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. To show Pythagoras Theorem can be used to find the length of a line. 1. Apply Pythagoras Theorem to find length of a line. 2. Show all working. 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

30 -Nov-20 www. mathsrevision. com National 4 REL 1. 2 a Created by Mr. Lafferty Maths Dept. Discuss with your partnerthe Finding how we might find the Length of a Line length of the line. 8 7 6 5 4 3 2 1 (7, 7) 3 5 (2, 4) 0 1 2 3 4 5 6 7 8 9 10

Created by Mr. Lafferty Maths Dept. 30 -Nov-20 www. mathsrevision. com National 4 REL 1. 2 a Pythagoras Theorem to find the length of a Line 8 7 6 (0, 6) 5 4 5 3 2 1 9 (9, 1) 0 1 2 3 4 5 6 7 8 9 10

Pythagoras Theorem to find the length of a Line www. mathsrevision. com National 4 REL 1. 2 a Now try Extension Booklet 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com National 4 REL 1. 2 a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.

Pythagoras Theorem www. mathsrevision. com National 4 REL 1. 2 a Learning Intention Success Criteria 1. To use knowledge already gained on Pythagoras Theorem to solve mixed problems using appropriate version of Theorem. 30 -Nov-20 1. Use the appropriate form Pythagoras Theorem to solving problems. Compiled by Mr. Lafferty Maths Dept.

Pythagoras Theorem National 4 REL 1. 2 a www. mathsrevision. com Finding hypotenuse c c a Finding shorter side a 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept. b Finding shorter side b

N G H O C D E F M J I K Q A R V T A W r L C U P Z S B o P(x, y)

Pythagoras Theorem www. mathsrevision. com National 4 REL 1. 2 a Now try Extension Booklet 30 -Nov-20 Compiled by Mr. Lafferty Maths Dept.