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

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

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

4. 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. (2) If a number is even then the number divides by two exactly. (3) If you have thrown a double six with a dice then your score with the dice is twelve. (4) If you have thrown a three and a four then your total score is seven with a dice. False True False

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

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

7. Is the triangle below right angled ? 6.9 9.2 11.5(1) Which side is the longest side ? 11.5 (2) Add the sum of the squares of the two shorter sides. 6.9 2 + 9.2 2 (3) Square the longest side separately. 11.5 2 (4) Are the two calculations equal to each other? = 47.61+84.64 132.25 =132.25 yes As 6.9 2 + 9.2 2 = 11.5 2 then by the converse of Pythagoras the triangle is right angled.

8. Is the triangle below right angled ? 8.1 10.8 14.5(1) Which side is the longest side ? 14.5 (2) Add the sum of the squares of the two shorter sides. 8.1 2 + 10.8 2 (3) Square the longest side separately. 14.5 2 (4) Are the two calculations equal to each other? = 65.61+116.64 210.25 =182.25 No. As 6.9 2 + 9.2 2  11.5 2 then by the converse of Pythagoras the triangle is not right angled.

9. What Goes In The Box ? 2. Use the converse of Pythagoras to determine if these triangles are right angled or not. (1) 13 5 12 (2) 39 28.8 23.4 (3) 107.9 41.5 99.6 (4) 49 117.6 123.5 Yes No Yes No