Pythagoras’ theorem
8.01
Understanding
1. a2 + b2 = c2
c isthehypotenuse.
2.a.Hypotenuseisthelongestside. ∴ 25 b.Tworemainingsides.7and24
3.Hypotenuseisthelongestsideandalso thesideoppositeoftherightangle.
a. Z
b. M
c. Y
d. C
Fluency
4.a.32 +42 =9+16 =25
b.52 =5 × 5 =25
c.Yesbecause32 +42 =52
5.a.172 +102 =289+100 =389 232 =23 × 23 =529
→ 172 +102 =232
∴ No
b.122 +352 =144+1225 =1369
372 =37 × 37 =1369
→ 122 +352 =372
∴ Yes
c.92 +162 =81+256 =337 182 =18 × 18 =324
→ 92 +162 =182
∴ No
d.12 +12 =1+1 =2 (√2)2 = √2 × √2 =2
→ 12 +12 =(√2)2
∴ Yes
6.Equation: a2 + b2 = c2
a.Hypotenuse: c
∴ 122 +92 = c2
b.Hypotenuse:26
∴ 102 + b2 =262
c.Hypotenuse:19
∴ x2 +132 =192
d.Hypotenuse: c
∴ 92 +32 = c2
7.a.62 +82 =36+64 =100
132 =13 × 13 =169 → 100 =169
∴ No
b.32 +42 =9+16 =25
52 =5 × 5 =25
→ 32 +42 =52
∴ Yes
c.22 +42 =4+16 =20
62 =6 × 6 =36 → 20 =36
∴ No
d.52 +122 =25+144 =169
132 =13 × 13 =169
→ 52 +122 =132
∴ Yes
8.Lastnumberishypotenuse.
a. x 2 +152 =172 x 2 +225=289 x 2 =64 x =8
b.72 + x 2 =252
49+ x 2 =625 x 2 =576 x = √576 x =24
c.282 + x 2 =532
784+ x 2 =2809 x 2 =2025 x =45
d.142 +482 = x 2
196+2304= x 2 x 2 =2500 x =50
9.a.82 +132 =64+169 =233 192 =19 × 19 =361 → 233 =361
∴ No
b.92 +162 =81+256 =337
252 =25 × 25 =625 → 337 =625
∴ No
c.202 +212 =400+441 =841
292 =841 → 202 +212 =292
∴ Yes
∴ No
10.a. x 2 +962 =1002 x 2 +9216=10000 x 2 =784 x = √784 x =28
b.222 +1202 = x 2
484+14400= x 2 x 2 =14884 x = √14884 x =122
c. x 2 +82 =102 x 2 +64=100 x 2 =36 x = √36 x =6
d.82 + x 2 =172
64+ x 2 =289 x 2 =225 x = √225 x =15
e. x 2 +402 =412 x 2 +1600=1681 x 2 =81 x = √81 x =9
Reasoning
11.Refertoanswerkey.
12.Refertoanswerkey.
13.Refertoanswerkey.
Problem-solving
14.Right-angledtrianglemeanstheoppositesideoftherightangle(hypotenuse) isthelongestside.
∴ FloreyandGiralang
15.a.202 +482 =400+2304 =2704
522 =52 × 52 =2704
→ 202 +482 =522
∴ Yes
b.20+48+52=120m
c.i.302 +402 =900+1600 =2500
502 =50 × 50 =2500
→ 302 +402 =502
∴ Yes
ii.262 +412 =676+1681 =2357
532 =53 × 53 =2809
→ 2357 =2809
∴ No
iii.142 +482 =196+2304 =2500
502 =50 × 50 =2500
→ 142 +482 =502
∴ Yes
iv.242 +452 =576+2025 =2601
512 =51 × 51 =2601
→ 242 +452 =512
∴ Yes
16. 20 a b
a 2 + b2 =202
a 2 + b2 =400
Usingtrialanderror:
a and b =12and16
17. 65 a b
a 2 + b2 =652
a 2 + b2 =4225
Usingtrialanderror:
a and b =39, 52or25, 60