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Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem S3 Credit Investigating Pythagoras Theorem Finding the length of the smaller side Solving Real – Life Problems www.mathsrevision.com Pythagoras Theorem Twice Converse of Pythagoras Theorem 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Starter Questions Q1. Explain why 4 + 6 x 5 = 34 and not 50 Q2. Calculate www.mathsrevision.com Q3. Does x2 – 121 factorise to (x – 11) (x - 11) Q4. The cost of an iPod is £80 including VAT. How much is the iPod BEFORE VAT. NON-CALCULATOR 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. 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. ‘ www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles What is the length of a ? 3 What is the length of b ? 4 www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 5 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles What is the length of a ? 6 What is the length of b ? 8 www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 10 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles What is the length of a ? 5 What is the length of b ? 12 www.mathsrevision.com Copy the triangle into your jotter and measure the length of c 13 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles Copy the table below and fill in the values that are missing a b c a2 b2 c2 3 4 5 12 13 6 8 10 www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Right – Angle Triangles Can anyone spot a relationship between a2, b2, c2. a b c a2 b2 c2 3 4 5 9 16 25 12 13 144 169 6 8 10 36 64 100 www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Pythagoras’s Theorem c b www.mathsrevision.com a 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Pythagoras’s Theorem x www.mathsrevision.com y z 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Summary of Pythagoras’s Theorem www.mathsrevision.com Note: The equation is ONLY valid for right-angled triangles. 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Calculating Hypotenuse Credit Learning Intention Success Criteria Use Pythagoras Theorem to calculate the length of the hypotenuse “the longest side” Know the term hypotenuse “ the longest side” Use Pythagoras Theorem to calculate the hypotenuse. www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Calculating Hypotenuse Credit Two key points when dealing with right-angled triangles The longest side in a right-angled triangle is called The HYPOTENUSE The HYPOTENUSE is ALWAYS opposite the right angle www.mathsrevision.com c2 = a2 + b2 (xz)2 = (xy)2 + (yz)2 a b c y x z 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Calculating the Hypotenuse Example 1 Q2. Calculate the longest length of the right- angled triangle below. c 8 www.mathsrevision.com 12 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Calculating the Hypotenuse Example 2 Q1. An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present which is 15km from the airport. It is at a height of 8km. How far away is the plane from the airport? A www.mathsrevision.com LA = 8 G L Airport GL = 15 Lennoxtown 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Calculating Hypotenuse Credit Now try Ex 2.1 and 2.2 MIA Page 147 www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. S3 Starter Questions S3 Credit www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side Credit Learning Intention Success Criteria 1. To show how Pythagoras Theorem can be used to find the length of the smaller side. Use Pythagoras Theorem to find the length of smaller side. 2. Show all working. www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side Credit 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 www.mathsrevision.com 20cm 12cm a cm 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Length of the smaller side Credit Example : Find the length of side a ? 10cm b cm 8 cm www.mathsrevision.com Check answer ! Always smaller than hypotenuse 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

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

Compiled by Mr. Lafferty Maths Dept. Length of smaller side S3 Credit Now work through Ex3.1 and Ex 3.2 Odd Numbers Only www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. S3 Starter Questions S3 Credit www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Solving Real – Life Problems Using Pythagoras Theorem Credit Learning Intention Success Criteria 1. To show how Pythagoras Theorem can be used to solve real-life problems. Apply Pythagoras Theorem to solve real-life problems. 2. Show all working. www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems Credit 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 height of the tree ? www.mathsrevision.com 17m 8m rod a c b 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems Credit Example 2 A garden has a fence around its perimeter and along its diagonal as shown below. What is the length of the fence from D to C. A B www.mathsrevision.com 13m 5m D C b m 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. Length of smaller side S3 Credit Now work through Ex4.1 and Ex 4.2 Odd Numbers Only www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. S3 Starter Questions S3 Credit www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Pythagoras Theorem Twice Credit Learning Intention Success Criteria 1. To use knowledge already gained on Pythagoras Theorem to solve harder problems using Theorem twice. Use the appropriate form of Pythagoras Theorem to solving harder problems. 2. Show all working. www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Solving Real-Life Problems Credit Problem : Find the length of h. Find length BD first h B C 15 www.mathsrevision.com 12 A D 13 19-Apr-17

Solving Real-Life Problems Credit Problem : Find the length of length y. Now find h h B C 15 www.mathsrevision.com 12 A D 13 19-Apr-17

Solving Real-Life Problems Credit Problem : Find the diagonal length of the cuboid AG. Find AH first F G B C 7cm www.mathsrevision.com E H 10cm 6cm A D 8cm 19-Apr-17

Solving Real-Life Problems Credit Problem : Find the diagonal length of the cuboid AG. Now find AG F G B C 7cm www.mathsrevision.com E H 10cm 6cm A D 8cm 19-Apr-17

Compiled by Mr. Lafferty Maths Dept. Pythagoras Theorem S3 Credit Now try Ex 5.1 Ch8 (page 154) www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Compiled by Mr. Lafferty Maths Dept. S3 Starter Questions S3 Credit www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Credit Learning Intention Success Criteria 1. To explain the converse of Pythagoras Theorem to prove a triangle is right-angled. Apply the converse of Pythagoras Theorem to prove a triangle is right-angled. www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Converse1 – talk Converse2 – opposite, reverse Converse of Pythagoras Theorem S3 Credit c Converse Theorem states that if b a www.mathsrevision.com 1. Then triangle MUST be right-angled. 2. Right-angle is directly opposite C. Hypotenuse 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Credit Problem : Is this triangle right-angled ? Explain Answer If it is then Pythagoras Theorem will be true 10cm 6 cm www.mathsrevision.com 9 cm By the Converse Theorem, triangle is NOT right-angled 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Credit Problem : A picture frame manufacturer claims that his are rectangular is his claim true. If it is then Pythagoras Theorem will be true 50cm 40 cm www.mathsrevision.com 30 cm By the Converse Theorem, frame IS rectangular 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Credit Now try Ex 6.1 & 6.2 Ch8 (page 156) www.mathsrevision.com 19-Apr-17 Compiled by Mr. Lafferty Maths Dept.