Understanding Engineering Mathematics

5.3.3 Triangles and their elementary properties

A. Other angle External angle

(i) 103 ° 77 °

(ii) 86 ° 94 °

(iii) 144 ° 36 °

(iv) 30 ° 150 °

B. (i) 25°,66°,89° (ii) 63°, 100°,17°

(iii) 45°, 115°,20° (iv) 27°,65°,88°

C. (i)a=b=c= 60 °,d= 120 ° (ii)a=b=d=f= 59 °,c=e= 62 °

5.3.4 Congruent triangles

(i) ADBandCBDare congruent

(ii) ADC,ABCcongruent

(iii) Not congruent

(iv) Not congruent

5.3.5 Similar triangles

A. (i)PR= 0 .7cm PQ= 0. 7 6cm ̇
(ii) PR= 1 .4cm PQ= 1. 5 3cm ̇
(iii)PR= 2 .45 cm PQ= 2. 68 3cm ̇
(iv)PR= 2 .1m PQ= 3. 0 6m ̇
B. (i) PQ= 1. 1 3cm ̇ PR= 0. ̇6cm BC=3cm
(ii) PQ= 0 .73 cm (2dp) PR= 0 .43 cm BC= 4 .6cm ̇
(iii) PQ= 4. 5 3cm ̇ PR= 2. ̇6cm BC= 0 .75 cm

5.3.6 The intercept theorem

(i) DC= 2. 29 (ii) EB= 1. 3 ̇ (iii) AD= 1. 5

(iv) AE= 1. 75

5.3.7 The angle bisector theorem

(i) x=2,y= 1 (ii) z= 1. 375

(iii) u= 1. 36 (iv) CD= 1. 53

5.3.8 Pythagoras’ theorem

A.(a) (i)

√

34 (ii) 13 (iii)

√

1201

(iv)

√

353 (v) 5