This document provides examples and questions about Pythagoras' theorem and applying it to find missing lengths in right triangles. It asks the reader to: 1) Name the hypotenuse of sample right triangles 2) Write the relationships between sides using Pythagoras' theorem 3) Use the theorem to find missing lengths 4) Determine if triangles are right, obtuse, or acute based on side lengths 5) Calculate the area of a shaded region in a rectangle

1. CH
AP
T ER
6
Pythagoras’ Theorem
1. Name the hypotenuse of the following right-angled triangles.
b
c
a
a
b
2. Write down the relationship between the sides of the following triangle.
U
V
TV2 = _______________
T
SV2 = _______________
W
S
3. By using Pythagoras teorem, find the value of x.
Q
6 cm R
12 cm
S
ͱ⒓cm
x
13 cm
P
4. Find the value of x.
3x cm
8 cm
17 cm
5. Find the values of x and y in each of the following figures.
(a)
(b)
P
Q
12 cm
15 cm
P
2 cm
S
R x cm S
y cm
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10
13 cm
y cm
6 cm
Q
30
cm
x cm
T
7 cm
R

2. 6.
P
Q
13 c
15 cm
m
S
T
9 cm
R
The diagram shows a rectangle. Find the area of the shaded region.
7. Determine whether the following triangle is a right-angled triangle.
R
ͱ⒓ cm
41
Q
ͱ⒓ cm
5
P
6 cm
8. Determine whether the following triangle is an obtuse-angled or acute-angled triangle.
P
10 cm
9 cm
Q
13 cm
R
9. Mr Samy tries to dig a rectangular pool of 8 m by 15 m. When he measures the diagonal,
it is 18 m. Is the pool rectangular in shape?
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