15-aug-15compiled by mr. lafferty maths dept. pythagoras theorem revision of simple pythagoras...

19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

Pythagoras Pythagoras TheoremTheorem

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Revision of simple Pythagoras Theorem

Converse of Pythagoras Theorem

3D - Pythagoras Theorem

Exam Questions

Starter QuestionsStarter Questionsw

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Given the two straight lines

3y + 2x - 12 = 0 4x + 6y = -24

In pairs explain what they have in commonAnd where each cross the x-axis and y-axis.

19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Know the term Know the term hypotenuse hypotenuse “ the “ the longest side”longest side”

1. We are revising Pythagoras Theorem

2.2. Use Pythagoras Theorem Use Pythagoras Theorem to calculate both the to calculate both the hypotenuse and smaller hypotenuse and smaller sides of a right-angled sides of a right-angled triangle.triangle.

Revision of Pythagoras Revision of Pythagoras TheoremTheorem

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Two key points when dealing with right-angled triangles

The longest side in a right-angled triangle is calledThe HYPOTENUSE

The HYPOTENUSE is ALWAYS opposite the right angle

b cc2 = a2 + b2

(xz)2 = (xy)2 + (yz)2

Example : A steel rod is used to support a treewhich is in danger of falling down.

What is the height of the tree ?

When coming across a problem involving When coming across a problem involving finding a missing side in a right-angled triangle, finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem you should consider using Pythagoras’ Theorem to calculate its length.to calculate its length.

2 2 2c a b

2 2 217 - 8a

2 225a

225 15a m

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Example 2Example 2A garden has a fence around its perimeter and A garden has a fence around its perimeter and along its diagonal as shown below. along its diagonal as shown below. What is the length of the fence from D to C.What is the length of the fence from D to C.

2 2 2( ) ( ) ( )AC DC AD

2 2 2( ) 13 - 5DC

2( ) 144DC

144 12DC m

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MTH 4-16a

19 Apr 2023Created by Mr. Lafferty Maths

Dept.w

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1 32 540

1 32 40

5 76 8 9 10

Finding the Length of a Line

Discuss with your partner how we might find the length of the

2 2 2c a b

2 2 25 3c

19 Apr 2023Created by Mr. Lafferty Maths

Dept.w

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1 32 540

1 32 40

5 76 8 9 10

2 2 2c a b

2 2 25 9c

25 81c

Pythagoras Theorem to find the length of a LineMTH 4-16a

19 Apr 202319 Apr 2023

Problem : Find the length of h.

2 2 2( ) ( ) ( )BD AD AB

2 2 2( ) 15 13BD

2( ) 394BD

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Find length BD first

19.85BD

19 Apr 202319 Apr 2023

Problem : Find the length of length y.

2 2 2( ) ( ) ( )BC BD DC

2 2 2( ) ( )h BD DC

2 2 2(19.85) (12)h

2 394 144h

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Now find h

23.2 ( 1 . .)h to d p

19 Apr 202319 Apr 2023ww

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NOTE !!!!

Pythagoras Theorem tends to pop up within circle type question

C D E F

P(x,y)

Now try N5 TJEx5.1

Ch5 (page 44)

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2 2 2 2

(1 )(2 3 )

1 1 16 7 42

2 515 3

1. True or false

2. Expand

3. Does factorise to

ab ba b a a b

Converse of Converse of Pythagoras Pythagoras

TheoremTheorem

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1.1. Apply the converse of Apply the converse of Pythagoras Theorem to Pythagoras Theorem to prove a triangle is prove a triangle is right-angled.right-angled.

1. We are learning the converse of Pythagoras Theorem to prove a triangle is right-angled.

2. Right-angle is directly opposite C.

TheoremTheorem

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2 2 2a +b =cb

Converse Theorem states that if

1. Then triangle MUST be right-angled.

Hypotenuse

Converse1 – talk

Converse2 – opposite, reverse

TheoremTheorem

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Problem : Is this triangle right-angled ? Explain Answer

2c =10210cm

2 2a +b

If it is then Pythagoras Theorem will be true.

2 2= 9 +6=81+36 = 117

2c =100

Since 117 ≠ 100 then by the Converse Theorem of

Pythagoras triangle IS NOT right-angled.

TheoremTheorem

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Problem : A picture frame manufacturer claims that his are rectangular is his claim true.

If it is then Pythagoras Theorem will be true

2c =5022 2a +b2 2= 30 +40

=900 +1600 = 2500

2c =2500

Since 2500 = 2500 then by the Converse Theorem of Pythagoras triangle IS

right-angled.

Now try N5 TJEx5.2

Ch5 (page 46)

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TheoremTheorem

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4 , 3 2

3 1 15 2 74 8 8

1. True or false

2. I f .

3. Factorise

p q and r

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1.1. Use the appropriate Use the appropriate form of Pythagoras form of Pythagoras Theorem to solving 3D Theorem to solving 3D problems.problems.

1. We are learning how to apply knowledge already gained on Pythagoras Theorem to solve 3D problems.

2.2. Show all working.Show all working.

3D Pythagoras 3D Pythagoras TheoremTheorem

19 Apr 202319 Apr 2023

Problem : Find the diagonal length of the cuboid AG.

2 2 2( ) ( ) ( )AH AD DH

2 2 2( ) 8 6AH

2( ) 64 36AH

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Find AH first

10AH cm A

19 Apr 202319 Apr 2023

Problem : Find the diagonal length of the cuboid AG.

2 2 2( ) ( ) ( )AG AH HG

2 2 2( ) 10 7AG

2( ) 100 49AG

2( ) 149AG

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Now find AG

12.2 ( 1 . .)AG cm to d p

Now try N5 TJEx5.3

Ch5 (page 47)

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15-aug-15compiled by mr. lafferty maths dept. pythagoras theorem revision of simple pythagoras...

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