Triangles Right-Angled Converse Theorem Illustrated
Explore examples and worked exercises to determine if triangles are right-angled using the converse of the Pythagoras theorem. Justify your conclusions with intelligent practice exercises.
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The Converse of The Converse of Pythagoras Theorem Pythagoras Theorem Silent Teacher Intelligent Practice Your Turn Narration Are the triangles right-angled? 55?? 12?? 48?? 5?? Example 72?? 20??
Worked Example Your Turn Are the triangles below right-angled? Are the triangles below right-angled? ?? ???? ?2+ ?2= 2 (60)2+(80)2= (100)2 ?? ???? ?2+ ?2= 2 (48)2+(55)2= (72)2 55?? 0.8? 60?? 48?? 3600 + 6400 = 10 000 2304 + 3025 = 5184 10 000 = 10 000 5329 5184 1? 72?? ?? ?? ? ??? ? ?????? ???????? ?? ?? ??? ? ??? ? ?????? ???????? ?? ???? ?? ???? ?2+ ?2= 2 (20)2+(21)2= (29)2 ?2+ ?2= 2 (5)2+(12)2= (20)2 12?? 21?? 5?? 20?? 400 + 441 = 841 25 + 144 = 400 841 = 841 169 400 20?? ?? ?? ? ??? ? ?????? ???????? 29?? ?? ?? ??? ? ??? ? ?????? ???????? @MrDraperMaths
Justify whether or not the triangles below are right-angled. 3?? 4) 1) 15?? 7?? 15?? 2) 8?? 39?? 17?? 3) 10?? 18?? 10?? 200?? 5) 89?? 80?? 7) 72?? 10?? 84?? 97?? 6) 10?? 91?? 60?? 10) 35?? 65?? 8) 12?? 85?? 50?? 36?? 5?? 9) 0.37? 0.03? 0.12? 11) 77?? 40?? 35?? @MrDraperMaths
Justify whether or not the triangles below are right-angled. 15?? 4) 1) 2) 7 2?? 2?? 4 2?? 10?? 3 2?? 2?? 9 3?? 3) 7 2?? 2 2?? 2?? 2?? 3?? 5) 21?? 7?? 6) 5 7?? 8) 7) 10?? 5 5?? 5 7?? 21?? 11?? 5 4?? 5 14?? 5 3?? 9) 5 2?? 10) (5 + 2)?? 11) 5 4?? 4 2?? 5 3?? (4 + 2)?? 5 7?? 3 2?? (3 + 2)?? @MrDraperMaths
Justify whether or not the triangles below are right-angled. 3?? 4) 1) 15?? 7?? 15?? 2) 8?? 39?? 17?? 3) 10?? 18?? 10?? 200?? 5) 89?? 80?? 7) 72?? 10?? 84?? 97?? 6) 10?? 91?? 60?? 10) 35?? 65?? 8) 12?? 85?? 50?? 36?? 5?? 9) 0.37? 0.03? 0.12? 11) 77?? 40?? 35?? @MrDraperMaths
Justify whether or not the triangles below are right-angled. 15?? 4) 1) 2) 7 2?? 2?? 4 2?? 10?? 3 2?? 2?? 9 3?? 3) 7 2?? 2 2?? 2?? 2?? 3?? 5) 21?? 7?? 6) 5 7?? 8) 7) 10?? 5 5?? 5 7?? 21?? 11?? 5 4?? 5 14?? 5 3?? 9) 5 2?? 10) (5 + 2)?? 11) 5 4?? 4 2?? 5 3?? (4 + 2)?? 5 7?? 3 2?? (3 + 2)?? @MrDraperMaths
