2. Converse of Pythagoras Geometry

3. Converse of Pythagoras In a triangle with sides a, b and c where c is the largest side, if a 2 +b 2 =c 2, then the triangle is right angled at C. a c b Use the above result to check each triangle below to see if it is right angled. 5cm 12cm 13cm 6cm 8cm 10cm

4. 5.3cm 4.2cm 3.7cm 3.5cm 8.2cm 8.6cm 5.1cm 9.3cm 7.8cm 9.8cm 5.7cm 8cm Use the result to check each triangle below to see if it is right angled.

5. d 24.5cm 32cm 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?

6.  25m 24m 7m   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.

7. 32′′ 24′′ 21.2′′ television screen 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?

8. In the diagram PS=4cm, SR=9cm and SQ = 6cm. Use Pythagoras to calculate the lengths of PQ and QR. Hence prove that triangle PQR is right angles at Q. 9cm4cm S Q R P 6cm

9. 16m 9m rope flag 13m ground 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?

10. 5cm 8cm 9cm 12cm 13cm 15cm 17cm 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?

11. 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. Coordinates

12. C A B 55m 56m 54m 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?

13. ba Q R P c Show that for triangle PQR to be right angled at Q, we require c=√ ab.