The Converse Of Pythagoras.

14m

19m

23m

Is the triangle right angled

or not ?

©Microsoft Word clipart

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 angles of the shape add up to 180oThen

the shape is a triangle.

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

a shape is a square.Then

the angles add up to 360o

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.

(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

True

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.

a given triangle is right angledThen

This converse is true and allows us to find right angled triangles.

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.

102

(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.

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.

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.

What Goes In The Box ? 2.Use the converse of Pythagoras to determine if these triangles are right angled or not.

(1) 135

12

(2)

3928.8

23.4

(3) 107.941.5

99.6

(4)

49

117.6

123.5

YesNo

Yes

No