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6

Determine whether each of the following triangles is a right-angled triangle.
(a) D 24 cm (b) S 20 cm
E
12 cm U
25 cm 7 cm 18 cm
F T

(a) The longest side = 25 cm (b) The longest side = 20 cm
Thus, 25 = 625 Thus, 20 = 400
2
2
24 + 7 = 576 + 49 18 + 12 = 324 + 144
2
2
2
2
= 625 = 468
Hence, DEF is a right-angled Hence, STU is not a right-angled
triangle. triangle.
Self Practice 13.2a

1. Determine whether each of the following triangles is a right-angled triangle.
(a) 15 cm (b) (c) 32 cm
18 cm 34 cm
17 cm 8 cm 40 cm 24 cm
30 cm

How do you solve problems? LEARNING
STANDARDS
Solve problems involving
7 the converse of the
S Pythagoras’ theorem.
In the diagram, calculate
the value of x. 28°
29 cm 20 cm
Q x

P 21 cm 155° R

CHAPTER
2
2
2
20 cm, 21 cm and 29 cm satisfy c = a + b . A housing contractor and
a civil engineer will use
Thus, ∠PQS = 90° the Pythagoras’ theorem 13
∠ SQR = 360° – 90° – 155° to solve problems
= 115° involving right angles
in the construction
x = 180° – 115° – 28° of buildings.
= 37°

301
The Pythagoras’ Theorem

13 TB Math F1.indd 301 11/10/16 12:22 PM