Transcript The Converse Of Pythagoras.

The Converse Of Pythagoras.
23m
Is the triangle
right angled
or not ?
14m
19m
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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
Then
the shape is a triangle.
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
Then
the angles add up to 360o
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
Then
a given triangle is right angled
a2 + b2 = c2 for a triangle.
Write the converse statement.
If
Then
a2 + b2 = c2 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 ?
10m
6m
8m
62+82
= 36 + 64
102
100
(1) Which side is the
longest side ?
10m
(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
(1) Which side is the
longest side ?
6.9
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
(1) Which side is the
longest side ?
8.1
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
39
Yes
No
12
(3)
41.5
107.9
(4)
123.5
49
Yes
99.6
117.6
No