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Answer:
MEP Y8 Practice Book A
62
4. (a) Use an accurate construction to find out if a triangle with sides of
lengths 6 cm, 7 cm and 12 cm contains a right angle.
(b) Use Pythagoras' Theorem to check your answer to part (a).
5. Ahmed draws a square with sides of length 6 cm.
He then measures a diagonal as 8.2 cm.
Use Pythagoras' Theorem to decide if Ahmed
has drawn the square accurately.
6. An isosceles triangle has 2 sides of length 8 cm.
The length of the base is 9 cm.
Decide, by calculation, whether the angle θ is
a right angle, an acute angle or an obtuse angle.
Show clearly how you reached your conclusion.
7. Measure the lengths of the sides and diagonal of your textbook. Use your
measurements to decide whether the corners of your book are right-angled.
8. A triangle has sides of lengths 21 cm, 28 cm and x cm.
(a) Show that the triangle has a right angle if x = 35.
(b) For what values of x will the triangle contain an obtuse angle?
9. An isosceles triangle is known to have one side of length 18 cm and one side
of length 28 cm.
(a) Explain why the triangle cannot contain a right angle,
(b) Show, by calculation, that it is possible for the triangle to contain three
acute angles. Draw a sketch of the triangle in this case.
10. A right-angled triangle has two sides of lengths 24 cm and 32 cm. Use
Pythagoras' Theorem to calculate the length of the other side.