# Pythagoras Theorem www mathsrevision com Nat 5 Revision

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Pythagoras Theorem www. mathsrevision. com Nat 5 Revision of simple Pythagoras Theorem Converse of Pythagoras Theorem 3 D - Pythagoras Theorem Exam Questions 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions Nat 5 www. mathsrevision. com Given the two straight lines 3 y + 2 x - 12 = 0 4 x + 6 y = -24 In pairs explain what they have in common And where each cross the x-axis and y-axis. 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 Learning Intention 1. We are revising Pythagoras Theorem Success Criteria 1. Know the term hypotenuse “ the longest side” 2. Use Pythagoras Theorem to calculate both the hypotenuse and smaller sides of a right-angled triangle. 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 Two key points when dealing with right-angled triangles The longest side in a right-angled triangle is called The HYPOTENUSE is ALWAYS opposite the right angle c b c 2 = a 2 + b 2 (xz)2 = (xy)2 + (yz)2 x a 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept. y z

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 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 ? c 05 -Dec-20 17 m Compiled by Mr. Lafferty Maths Dept. rod 8 m b a

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 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 5 m D 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept. B 13 m bm C

05 -Dec-20 Discuss with your partnerthe Finding how we might find the Length of a Line length of the line. MTH 4 -16 a www. mathsrevision. com Created by Mr. Lafferty Maths Dept. 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. 05 -Dec-20 www. mathsrevision. com MTH 4 -16 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

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 Problem : Find the length of h. Find length BD first h B 15 A 05 -Dec-20 C 12 13 D

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 Problem : Find the length of length y. Now find h h B 15 A 05 -Dec-20 C 12 13 D

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 NOTE !!!! Pythagoras Theorem tends to pop up within circle type question 05 -Dec-20

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)

Revision of Pythagoras Theorem www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 5. 1 Ch 5 (page 44) 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com Nat 5 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem www. mathsrevision. com Nat 5 Learning Intention 1. We are learning the converse of Pythagoras Theorem to prove a triangle is right-angled. 05 -Dec-20 Success Criteria 1. Apply the converse of Pythagoras Theorem to prove a triangle is right-angled. Compiled by Mr. Lafferty Maths Dept.

Converse 1 – Converse talk www. mathsrevision. com Nat 5 of 2 – opposite, Pythagoras Theorem Converse reverse Converse Theorem states that if c b a 1. Then triangle MUST be right-angled. 2. Right-angle is directly opposite C. Hypotenuse 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem Since 117 ≠ 100 then by the Converse Theorem of Pythagoras triangle IS NOT right-angled. Nat 5 www. mathsrevision. com Problem : Is this triangle right-angled ? Explain Answer If it is then Pythagoras Theorem will be true. c 10 cm 9 cm b 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept. 6 cm a

www. mathsrevision. com Nat 5 Converse of Pythagoras Theorem Since 2500 = 2500 then by the Converse Theorem of Pythagoras triangle IS right -angled. Problem : A picture frame manufacturer claims that his are rectangular is his claim true. If it is then Pythagoras Theorem will be true a 40 cm 50 cm c 30 cm b 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Converse of Pythagoras Theorem www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 5. 2 Ch 5 (page 46) 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com Nat 5 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.

3 D Pythagoras Theorem www. mathsrevision. com Nat 5 Learning Intention 1. We are learning how to apply knowledge already gained on Pythagoras Theorem to solve 3 D problems. 05 -Dec-20 Success Criteria 1. Use the appropriate form of Pythagoras Theorem to solving 3 D problems. 2. Show all working. Compiled by Mr. Lafferty Maths Dept.

3 D Pythagoras Theorem www. mathsrevision. com Nat 5 Problem : Find the diagonal length of the cuboid AG. Find AH first F G B C E A 05 -Dec-20 10 cm 8 cm D 7 cm H 6 cm

3 D Pythagoras Theorem www. mathsrevision. com Nat 5 Problem : Find the diagonal length of the cuboid AG. Now find AG F G B C E A 05 -Dec-20 10 cm 8 cm D 7 cm H 6 cm

3 D Pythagoras Theorem www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 5. 3 Ch 5 (page 47) 05 -Dec-20 Compiled by Mr. Lafferty Maths Dept.