The Converse Of Pythagoras.

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Presentation transcript:

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

What Is A Converse ? Consider the sentence below: If the angles of the shape add up to 180o Then the shape is a triangle. To make the converse statement swap around the parts of the statement in the white box: If the shape is a triangle. Then the angles of the shape add up to 180o 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 360o Now make the converse statement. If the angles add up to 360o Then a shape is a square. Can you think of a shape with angles of 360o 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 then 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. The Theorem Of Pythagoras states: If a given triangle is right angled Then a2 + b2 = c2 for a triangle. Write the converse statement. If a2 + b2 = c2 for a triangle. Then 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 ? (1) Which side is the longest side ? 6m 8m 10m 10m (2) Add the sum of the squares of the two shorter sides. 6 2 + 8 2 102 (3) Square the longest side separately. = 36 + 64 100 =100 (4) Are the two calculations equal to each other? As 6 2 + 8 2 = 10 2 then by the converse of Pythagoras the triangle is right angled. yes

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 11.5 2 (3) Square the longest side separately. = 47.61+84.64 132.25 =132.25 (4) Are the two calculations equal to each other? As 6.9 2 + 9.2 2 = 11.5 2 then by the converse of Pythagoras the triangle is right angled. yes

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 14.5 2 (3) Square the longest side separately. = 65.61+116.64 210.25 =182.25 (4) Are the two calculations equal to each other? As 8.1 2 + 10.8 2  14.5 2 then by the converse of Pythagoras the triangle is not right angled. No.

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