[non right-angled triangles]

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Presentation transcript:

[non right-angled triangles] Pythagoras [non right-angled triangles] © T Madas

Non-right angled triangles C C C “Hypotenuse” “Hypotenuse” Hypotenuse B A A B A B RIGHT ANGLED OBTUSE TRIANGLE ACUTE TRIANGLE The hypotenuse squared is equal to the sum of the squares of the other two sides The hypotenuse squared is greater than the sum of the squares of the other two sides The hypotenuse squared is less than the sum of the squares of the other two sides © T Madas

Non-right angled triangles C OBTUSE TRIANGLE 92 42 + 72 9 81 7 16 + 49 81 > 65 A B 4 © T Madas

Non-right angled triangles C ACUTE TRIANGLE 82 62 + 72 64 36 + 49 6 8 64 < 85 A B 7 © T Madas

Determine what type each of these triangles is, given the lengths of their sides: 8, 10, 13 9, 11, 13 9, 40, 41 Longer side is 13 Longer side is 13 Longer side is 41 132 = 169 132 = 169 412 = 1681 102 + 82 = 112 + 92 = 402 + 92 = 100 + 64 = 121 + 81 = 1600 + 81 = 164 202 1681 OBTUSE TRIANGLE ACUTE TRIANGLE RIGHT-ANGLED TRIANGLE © T Madas

Classify the following triangle triples Classify the following triangle triples* into acute, right-angled and obtuse. *lengths of the 3 sides of triangles (2,4,5) (3,4,5) (1,3,5) (5,12,13) (7,20,25) (11,21,24) (7,24,25) (9,11,15) (9,14,19) (10,17,25) (8,15,17) (7,20,25) (11,21,30) (17,24,35) (20,21,29) (18,35,50) (9,13,20) (15,36,40) (9,40,41) (15,20,24) (11,60,61) © T Madas

© T Madas