The Converse Of Pythagoras 23 m Is the

The Converse Of Pythagoras. 23 m Is the triangle right angled or not ? 14 m 19 m ©Microsoft Word clipart

What Is A Converse ? Consider the sentence below: If the angles of the shape add up to 180 o Then the shape is a triangle. To make the converse statement swap around the parts of the statement in the white box: If Then the shape is a triangle. the angles of the shape add up to 180 o This is the converse statement.

Not all converse statements are true. Consider the sentence below: If a shape is a square Then the angles add up to 360 o Now make the converse statement. If Then the angles add up to 360 o a shape is a square. Can you think of a shape with angles of 360 o which is not a square ? Any closed quadrilateral.

What Goes In The Box ? Write the converse statement and decide if the converse of the statement is true or false. (1) If a shape is a square then the shape has parallel sides. False (2) If a number is even the number divides by two exactly. True (3) If you have thrown a double six with a dice then your score with the dice is twelve. True (4) If you have thrown a three and a four then your total score is seven with a dice. False

The Converse Of Pythagoras. Theorem Of Pythagoras states: If Then a given triangle is right angled a 2 + b 2 = c 2 for a triangle. Write the converse statement. If Then a 2 + b 2 = c 2 for a triangle. a given triangle is right angled This converse is true and allows us to find right angled triangles.

Testing For A Right Angled Triangle. Is the triangle below right angled ? 10 m 6 m 8 m 62+82 = 36 + 64 102 100 (1) Which side is the longest side ? 10 m (2) Add the sum of the squares of the two shorter sides. (3) Square the longest side separately. =100 As 6 2 + 8 2 = 10 2 then by the converse of Pythagoras the triangle is right angled. (4) Are the two calculations equal to each other? yes

Is the triangle below right angled ? 11. 5 6. 9 (1) Which side is the longest side ? 11. 5 9. 2 6. 9 2 + 9. 2 2 = 47. 61+84. 64 11. 5 2 132. 25 (2) Add the sum of the squares of the two shorter sides. (3) Square the longest side separately. =132. 25 As 6. 9 2 + 9. 2 2 = 11. 5 2 then by the converse of Pythagoras the triangle is right angled. (4) Are the two calculations equal to each other? yes

Is the triangle below right angled ? 14. 5 8. 1 (1) Which side is the longest side ? 14. 5 10. 8 8. 1 2 + 10. 8 2 = 65. 61+116. 64 14. 5 2 210. 25 (2) Add the sum of the squares of the two shorter sides. (3) Square the longest side separately. =182. 25 As 6. 9 2 + 9. 2 2 11. 5 2 then by the converse of Pythagoras the triangle is not right angled. (4) Are the two calculations equal to each other? No.

What Goes In The Box ? 2. Use the converse of Pythagoras to determine if these triangles are right angled or not. (1) (2) 13 5 23. 4 28. 8 Yes 39 No 12 (3) 41. 5 107. 9 (4) 123. 5 49 Yes 99. 6 117. 6 No