Converse of Pythagoras

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Converse of Pythagoras

• Geometry

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Converse of Pythagoras In a triangle with sides
a, b and c where c is the largest side, if
a2b2c2, then the triangle is right angled at
C.
Use the above result to check each triangle
below to see if it is right angled.
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Use the result to check each triangle below to
see if it is right angled.
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A rectangular picture frame is to be made. It is
32cm high and 24.5cm wide as shown in the
diagram. To check that the frame is rectangular,
the diagonal, d, is measured. It is found to be
39.6cm. Is the frame rectangular?
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Long ago farmers made right angles using a long
rope with knots in it as shown in the diagram.
Explain how a farmer might check that a field is
rectangular using the piece of rope shown.
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The diagram shows a 32 inch television screen.
The size of a television screen is given as the
length of the diagonal. Is the screen
rectangular?
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In the diagram PS4cm, SR9cm and SQ 6cm. Use
Pythagoras to calculate the lengths of PQ and
QR. Hence prove that triangle PQR is right
angles at Q.
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A flagpole is 9m long. A rope holds the
flagpole in position. The rope is 16m long and
is fixed to the ground 13m from the foot of the
pole. Is the flagpole vertical?
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A pupil has 7 sticks of different lengths as
shown. If he picks three of them and forms a
triangle, how many different triangles can he
form? How many of these triangles will be right
angled?
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Coordinates
Prove that the shape formed by joining the 4
points A(-2,0), B(0,4), C(8,0) and D(6,-4) is a
rectangle.
On square paper plot the points A(0,2), B(6,4)
and C(8,-2). Use Pythagoras to find the length
of the sides of the triangle ABC. Use the
converse of Pythagoras to show that the triangle
ABC is right angled at B.
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The diagram shows part of the structure for
supporting a bridge. It is essential that angle
ABC is right angled if the bridge is to be
supported properly. Is this the case with the
support shown?
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Show that for triangle PQR to be right angled
at Q, we require cv ab.