Revision questions
8A Core skills 1. (i) 58°, straight angle followed by corresponding angle
(ii) 30°, isosceles triangle followed by 3 angles in a triangle
(iii) 55°, 3 angles of a triangle sum to 180°
(iv) 81°, straight angle equals 180° (v) 31°, vertically opposite, opposite angles in a parallelogram, three angles in a triangle
(vi) 35°, alternate followed by three angles in a triangle
2. (i) x = 60°, equilateral triangle, 3 angles in a triangle
(ii) x = 42° (straight angle), y = 107° (straight angle), z = 31° (3 angles of a triangle)
(iii) x = 27° (straight then corresponding), y = 119° (straight then corresponding), z = 92° (3 angles in a triangle)
(iv) x = 115° (straight then corresponding), y = 65° (corresponding), z = 65° (opposite angle in a parallelogram)
(v) x = 55° (straight angle), y = 39° (straight angle), z = 86° (3 angles in a triangle)
(vi) x = 35° (straight angle), y = 85° (straight angle), z = 30° (3 angles in a triangle)
3. Many valid answers 4. (i) 62°, alternate (ii) 71°, corresponding
5. (i) 65° (ii) 25°
6. (i) 57°, alternate (ii) 71°, straight angle, then corresponding
7. 71°, isosceles, 3 angles in triangle, corresponding
8. (i) 28°, alternate (ii) 64°, corresponding to y + 36°
10.(i)
(a) |∠ACB| = 100°, |∠CAB| = 40°, |∠CBA| = 40°
(b) They are equal (c)
(ii)
In an isosceles triangle, the angles opposite the equal sides are equal
(a) |∠DBC| = 140° (b) It is equal to the sum of the 2 internal opposite angles
(c) Each exterior angle of a triangle is equal to the sum of the two interior opposite angles
11.Congruent by SSS: |AB| = |BC|, given;
|AD| = |CD|, given; |BD| = |BD|, common side
12.Congruent by SAS: |AE| = |EC|, diagonals of a parallelogram bisect
each other; |∠AEB| = |∠DEC|, vertically opposite; |BE| = |ED|, diagonals of a parallelogram bisect each other
3. (ii) 4. (i)
8B Taking it further
1. (i) 30° (ii) 80°
2. (i) Many valid answers, e.g. ∠2 and ∠4
(ii) Many valid answers, e.g. ∠4 and ∠10
(iii) ∠2 and ∠10 (iv) ∠9 = 40° and ∠10 = 140°
3. (i) 40° (ii) 2x + 35 corresponds to 5x – 85
4. (i) x = 32, 2x = 64, x + 20 = 55, 3x − 35 = 61
(ii) x = 20, 3x + 15 = 75, 7x − 35 = 105, x + 55 = 75
(iii) x = 15, y = 4, 4x − 10 = 50, 2x + 5y = 50, 6x + 10y = 130
5. 152° 6. (i) 50° (ii) 60° (iii) 70°
7. 15°, 75° 8. 60°, all angles equal and sum to 180°
10.Congruent by ASA: |∠LAM| =
|∠CMN|, corresponding (AC is a transversal on BA∥NM); |AM| = |MC|, M is the midpoint of AC; |∠AML| = |∠MCN|, corresponding (AC is a transversal on BA∥NM)
Unit 9 Working with the coordinate plane
Practice questions 9.1 1. (i) B = (−3, 7); C = (−1, −6); D = (3, −3); E = (3, 4); F = (−5, −3); H = (−3, −2); I = (8 ,0); M = (−8, 8); N = (3, −9); O = (7, −8); P = (−8, 1); Q = (−3, 0); R = (6, −8); V = (0, 1); X = (−5, −9); Z = (6, 4)
(ii)
(a) First (b) Third (c) Second (d) Fourth
(a) Midpoint = (–1, 2) (b) Midpoint = (6, 4) (c) Midpoint = (–3, –3) (4, 7)
5. (i) (ii)
(ii) (3, 4) (iii) (4⋅5, −2⋅5) (iv) (−3⋅5, −7⋅5) (v) (0⋅5, −2⋅5) (vi) (−0⋅25, 4) (−4, −4) (8, −5)
(iii) (5, 2) (iv) (−6, −7) (v)
(−2, 6) (vi) (−3, 3) 6. (i) (−0⋅5, 2⋅5) (ii) (2⋅5, −0⋅5)
7. (i) Adam (4, 5); Barry (4, 2); Cillian (−3, 1)
(ii) School (0⋅5, 1⋅5) (iii) Swimming pool (0⋅5, 3) (iv) (−3, 4) and (−3, –2)
8. Diagonals bisect each other at (5, 2) 9. (3, 8) 10.(6, 4) 11.(3, 2), (6, 4), (9, 6), (12, 8) and (15, 10)
378 Linking Thinking 2
Practice questions 9.2
1. (i) 2√3 (ii) 3√3 (iii) 2√10
2. (i) 5⋅66 (ii) 13⋅45 (iii) 5 (iv) 4⋅12 (v) 14⋅87 (vi) 17⋅03
3. (i) √85 (ii) 5√2 (iii) √61
4. Point B 5. Scalene; all sides are different lengths 6. (i) (0, 6⋅5) (ii)
7. (i)
(ii) Radius = 2√13 (7.2), diameter = 4√13 (14.4)
8. (i) 10⋅44 m (ii) 9⋅22 m (iii) 18⋅87 m
9. 6√
_ 17or 24⋅7
10.(i) Opposite sides are equal in length
11.(i) 13√ 12.|AC|2
13.(i)
(ii) Diagonals not equal = |AB|2
_ 2 or 18·38
(−0⋅5, 4)
(ii) 6⋅8 km (iii) 16.3 km
Practice questions 9.3
1. (i) Positive (ii) Negative (iii) Zero (iv) Undefined (v) Positive (vi) Negative
2. (i) 1 (ii) −4
(iii) 0 (iv) 8
(v) 1 (vi) −9
3. (i) −7 (ii) −3
(iii) –1 (iv) 5
_ 8
(v) 4. (i)
_ 11
3
(vi) −2 1
_ 5
__ 4; D; goes up 1 (rise) for every 4 across (run)
(ii) −2; C; goes down 2 (negative rise) for every 1 across (run)
(iii) 0; E; doesn’t rise or fall (iv) 3; A; goes up 3 (rise) for every 1 across (run)
(v) −5 5 for 6 across
__ 6; B; goes down (negative rise)
5. The ramp, as it has a higher slope (0⋅75) than the hill (0.6
˙)
6. Points are collinear as the slope of AB = slope of BC = slope of AC
_ 5
_ 0 , undefined
_ 5
_ 3
_ 2
+ |BC|2
|AM| = 4.03, |MB| = 4.03 (3, −1)
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116 |
Page 117 |
Page 118 |
Page 119 |
Page 120 |
Page 121 |
Page 122 |
Page 123 |
Page 124 |
Page 125 |
Page 126 |
Page 127 |
Page 128 |
Page 129 |
Page 130 |
Page 131 |
Page 132 |
Page 133 |
Page 134 |
Page 135 |
Page 136 |
Page 137 |
Page 138 |
Page 139 |
Page 140 |
Page 141 |
Page 142 |
Page 143 |
Page 144 |
Page 145 |
Page 146 |
Page 147 |
Page 148 |
Page 149 |
Page 150 |
Page 151 |
Page 152 |
Page 153 |
Page 154 |
Page 155 |
Page 156 |
Page 157 |
Page 158 |
Page 159 |
Page 160 |
Page 161 |
Page 162 |
Page 163 |
Page 164 |
Page 165 |
Page 166 |
Page 167 |
Page 168 |
Page 169 |
Page 170 |
Page 171 |
Page 172 |
Page 173 |
Page 174 |
Page 175 |
Page 176 |
Page 177 |
Page 178 |
Page 179 |
Page 180 |
Page 181 |
Page 182 |
Page 183 |
Page 184 |
Page 185 |
Page 186 |
Page 187 |
Page 188 |
Page 189 |
Page 190 |
Page 191 |
Page 192 |
Page 193 |
Page 194 |
Page 195 |
Page 196 |
Page 197 |
Page 198 |
Page 199 |
Page 200 |
Page 201 |
Page 202 |
Page 203 |
Page 204 |
Page 205 |
Page 206 |
Page 207 |
Page 208 |
Page 209 |
Page 210 |
Page 211 |
Page 212 |
Page 213 |
Page 214 |
Page 215 |
Page 216 |
Page 217 |
Page 218 |
Page 219 |
Page 220 |
Page 221 |
Page 222 |
Page 223 |
Page 224 |
Page 225 |
Page 226 |
Page 227 |
Page 228 |
Page 229 |
Page 230 |
Page 231 |
Page 232 |
Page 233 |
Page 234 |
Page 235 |
Page 236 |
Page 237 |
Page 238 |
Page 239 |
Page 240 |
Page 241 |
Page 242 |
Page 243 |
Page 244 |
Page 245 |
Page 246 |
Page 247 |
Page 248 |
Page 249 |
Page 250 |
Page 251 |
Page 252 |
Page 253 |
Page 254 |
Page 255 |
Page 256 |
Page 257 |
Page 258 |
Page 259 |
Page 260 |
Page 261 |
Page 262 |
Page 263 |
Page 264 |
Page 265 |
Page 266 |
Page 267 |
Page 268 |
Page 269 |
Page 270 |
Page 271 |
Page 272 |
Page 273 |
Page 274 |
Page 275 |
Page 276 |
Page 277 |
Page 278 |
Page 279 |
Page 280 |
Page 281 |
Page 282 |
Page 283 |
Page 284 |
Page 285 |
Page 286 |
Page 287 |
Page 288 |
Page 289 |
Page 290 |
Page 291 |
Page 292 |
Page 293 |
Page 294 |
Page 295 |
Page 296 |
Page 297 |
Page 298 |
Page 299 |
Page 300 |
Page 301 |
Page 302 |
Page 303 |
Page 304 |
Page 305 |
Page 306 |
Page 307 |
Page 308 |
Page 309 |
Page 310 |
Page 311 |
Page 312 |
Page 313 |
Page 314 |
Page 315 |
Page 316 |
Page 317 |
Page 318 |
Page 319 |
Page 320 |
Page 321 |
Page 322 |
Page 323 |
Page 324 |
Page 325 |
Page 326 |
Page 327 |
Page 328 |
Page 329 |
Page 330 |
Page 331 |
Page 332 |
Page 333 |
Page 334 |
Page 335 |
Page 336 |
Page 337 |
Page 338 |
Page 339 |
Page 340 |
Page 341 |
Page 342 |
Page 343 |
Page 344 |
Page 345 |
Page 346 |
Page 347 |
Page 348 |
Page 349 |
Page 350 |
Page 351 |
Page 352 |
Page 353 |
Page 354 |
Page 355 |
Page 356 |
Page 357 |
Page 358 |
Page 359 |
Page 360 |
Page 361 |
Page 362 |
Page 363 |
Page 364 |
Page 365 |
Page 366 |
Page 367 |
Page 368 |
Page 369 |
Page 370 |
Page 371 |
Page 372 |
Page 373 |
Page 374 |
Page 375 |
Page 376 |
Page 377 |
Page 378 |
Page 379 |
Page 380 |
Page 381 |
Page 382 |
Page 383 |
Page 384 |
Page 385 |
Page 386 |
Page 387 |
Page 388 |
Page 389 |
Page 390 |
Page 391 |
Page 392 |
Page 393 |
Page 394 |
Page 395 |
Page 396 |
Page 397 |
Page 398 |
Page 399 |
Page 400 |
Page 401 |
Page 402 |
Page 403 |
Page 404 |
Page 405 |
Page 406
