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

2. 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.

3. 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.

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.
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

5. 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.

6. 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.
102
(3) Square the longest side separately. =
100
=100
(4) Are the two calculations equal to each other?
As = 10 2 then by the converse of Pythagoras the triangle is right angled.
yes

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

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

9. 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