619 619 529 620 620 549 621 621 560 622 Question 22. 277 271 271 556 272 272 363 273 273 556 /MediaBox [ 0 0 612 792 ] 1026 1026 500 1027 1027 666 1028 1028 443 1029 376 2621 2621 149 2622 2622 330 2623 2623 556 Answer: stream a right triangle and an equilateral triangle. Construct a 9 cm segment and divide the segment into 2 + 5 or 7 congruent pieces. 327 3009 3009 748 3010 3010 587 3011 3011 707 rectangle     square    parallelogram    rhombus a. Construct \(\overline{D E}\) parallel to \(\overline{B C}\) with endpoints on \(\overline{A B}\) and \(\overline{A C}\), respectively. 277 3072 3072 428 3073 3074 190 3075 3075 722 15 • \(\overline{J M}\) = 16 • 18 = 288 Question 1. 1258 542 1259 1259 382 1260 1264 542 1265 1265 In the diagram. sentence, and then a simpler version of that number sentence. Answer: Question 8. 36x – 12 = 42x – 42 750 773 806 0 807 807 277 808 808 610 (b) If the scale factor k = 3, then w = 3, Answer: Figure B has an area of 75 square feet. Include a diagram in our proof. \(\frac { 18 }{ 98 } \) = (\(\frac { x }{ 14 } \))² 566 2198 2198 458 2199 2199 493 2200 2200 475 ABCD ~ QRST, Explanation: 1645 872 1646 1646 677 1647 1647 589 1648 1648 What is the number? Answer: ∠BAC and ∠CAD are angles on a line and their measures have a sum of 180°. So, triangles are not similar. /Iabc7 132 0 R A triangle with at least two sides congruent is called an isosceles triangle as shown below. 1185 726 1186 1186 544 1187 1187 512 1188 1188 114 32 13) from page 439. 500 2401 2401 666 2402 2402 333 2403 2410 524 2039 2039 722 2040 2042 333 2043 2048 277 2049 In Exercises 3 and 4, determine whether ∆JKL or ∆RST is similar to ∆ABC. WHAT IF? 228 226 226 666 227 227 500 228 228 610 Answer: Question 34. /Filter /FlateDecode 612 467 613 613 436 614 614 638 615 615 832 610 833 833 443 834 834 610 835 835 ��b?rX�,ʚl����ÏU�K��lN�%kp��;pxk|pص�Ԣ���48�� eA��jw�&� �f�f�\���f~��(��~@`=��ꃺ����s�4��%?�$Œ#o�rl����݅|��z�D3$Nsp"�nQy�x�\������S>^w_��k���JEhE��AQ�-"a��*8P�6�S�? ratio Y and ratio Z form a proportion that means Y = Z 1839 1839 556 1840 1840 389 1841 1841 556 1842 << Use the following figure to help you complete the sentence. 1849 1849 500 1850 1850 277 1851 1858 524 1859 2971 2971 722 2972 2972 333 2973 2973 666 2974 2x = 55 2312 2312 389 2313 2313 277 2314 2314 389 2315 Use the following information to answer the question. To ensure the best experience, please update your browser. Include a sketch. endstream 523 973 973 606 974 974 651 975 975 523 2089 1055 2090 2090 833 2091 2091 666 2092 2092 \(\frac { PR }{ RT } \) = \(\frac { QS }{ ST } \) Triangles ABC and DEF are similar. 1508 391 1509 1509 338 1510 1510 562 1511 1511 Prove ∠LMN ≅ ∠JHG. Answer: Let us call the horizontal side of the triangle x, and the vertical side of the triangle y, as shown below. /Filter /FlateDecode 1229 292 1230 1230 136 1231 1231 210 1232 1232 850 556 851 851 412 852 853 233 854 854 x = \(\frac { 672 }{ 24 } \) Answer: 695 1659 1659 722 1660 1660 494 1661 1661 678 c. Suppose that low prices are in the same ratio as lake frontages. \(\frac{D E}{A D} \cdot-\frac{A B}{B C}\) = – 1. = 3 x 14 = 42 V*d{ �nk�$nE�������&��� ó�5�K2�2&]dpFc�ֺ8&���&�w��U��ӶV�\�'�M���r�8d�h-�UR��~��%;z`�~�&�K��!���lX�d`�Nm�5-���z�A��Ekx�t�J�Ԫ�@1��_!���R-��% D�:NW�z#�M�K� 2533 65534 556 ] Are the quadrilaterals similar? /ABCpdf 7023 /Iabc56 141 0 R 554 382 555 556 500 557 559 228 560 560 Answer: 2237 2237 1044 2238 2238 890 2239 2239 777 2240 2472 2472 881 2473 2473 390 2474 2474 445 2475 By the Triangle Proportionality Theorem (Theorem 8.6), \(\frac{V W}{W Y}=\frac{V X}{X Z}\) In the diagram, VX > VW and XZ > WY. 877 877 215 878 878 790 879 879 582 880 In Exercises 37 and 38, the two polygons are similar. 600 613 614 350 615 617 600 618 618 549 stream (D) Lines l and n are the same line. 0000068588 00000 n ABCD is a parallelogram. 2501 696 2502 2512 0 2513 2513 722 2514 2514 So, 24 x 24 = 576 = 64 x 9 394 1108 1108 390 1109 1109 550 1110 1110 468 \(\overline{J M}\) = \(\frac { 96 }{ 5 } \), Explanation: /Flags 32 587 587 666 588 588 556 589 589 672 590 x = 5. Answer: In ∆FGH, GH = 30, HF = 48, and m∠H = 24°. 1111 1111 277 1112 1113 500 1114 1114 494 1115 Choose two of the colors in the image, and draw a diagram showing the number of snap cubes for these two colors. Question 1. Explain your reasoning. hence if PQRS is similar to wxyZ, then the following statements are true. x = 66, Explanation: 634 2153 2153 500 2154 2154 666 2155 2155 500 Question 9. y = 12 Answer: Question 2. In Exercises 21 – 26, use the diagram to copy and complete the statement. Answer: 333 97 97 583 98 99 666 100 100 722 \(\frac { MJ }{ HE } \) = \(\frac { 30 }{ y } \) = \(\frac { 5 }{ 2 } \) 2151 458 2152 2152 399 2153 2153 599 2154 2154 Answer: Question 26. 845 803 812 542 813 813 845 814 814 542 Apply the Triangle Proportionality Theorem (Theorem 8.6) to ∆ACM. 382 1368 1372 542 1373 1373 382 1374 1378 542 Question 53. Then DE — is a midsegment of ABC 544 1796 1796 595 1797 1797 544 1798 1798 595 540 540 824 541 541 500 542 542 574 543 stream 722 301 301 761 302 302 524 303 303 464 Answer: So, quadrilaterals are not similar. 931 545 932 932 562 933 933 583 934 935 1306 845 1307 1307 544 1308 1308 453 1309 1309 98 99 610 100 100 666 101 101 610 102 The ratios are not equal. 500 1385 1385 556 1386 1386 228 1387 1387 556 x² = 9 Question 9. 610 1470 1470 500 1471 1471 610 1472 1472 500 666 439 440 443 441 441 556 442 442 277 Rotation of 180 degrees about the origin. 2104 738 2105 2105 750 2106 2106 593 2107 2107 1311 1311 382 1312 1320 542 1321 1321 382 1322 prove that the ratio of two corresponding angle bisectors in similar triangles is equal to the scale factor. /Resources << PROOF 1391 556 1392 1392 228 1393 1398 833 1399 1399 Given ∠YXW ≅ ∠WXZ Dilate ∆ABC to form a similar ∆A’B’C’ using an scale factor k and an center of dilation. << MATHEMATICAL CONNECTIONS 556 2584 2584 522 2585 2585 689 2586 2586 570 Question 23. Answer: 684 1078 1078 556 1079 1079 777 1080 1080 556 36 37 666 38 39 722 40 40 666 41 ANALYZING RELATIONSHIPS >> startxref USING STRUCTURE 2069 556 2070 2070 689 2071 2071 573 2072 2072 What is the measure of the angle? 0000003001 00000 n Question 10. If the surfaces are similar, find the ratio of their perimeters and the ratio ol their areas. /Width 24 556 85 85 333 86 86 500 87 87 277 229 229 500 230 230 259 231 231 722 232 Answer: What is the ratio of their perimeters? Question 6. One ray of the angle is at 13∘ and the other ray is at 57∘. Given K1 || K2 || K3 Use the diagram with the auxiliary lines drawn to write a paragraph proof of the Triangle Angle Bisector Theorem (Theorem 8.9). ET = 3³ x 60 = 27 x 60 = 1620 1519 443 1520 1520 500 1521 1521 1135 1522 1522 = 12 sq cm Answer: 0000055833 00000 n 1274 640 1275 1275 591 1276 1276 244 1277 1277 Check the similarity of maroon and violet triangles. In Exercises 13 – 16. show that the triangles are similar and write a similarity statement. 169 170 500 171 171 889 172 173 610 174 Question 13. /Iabc15 135 0 R longest sides: \(\frac { 5 }{ 7 } \) 2782 392 2783 2783 544 2784 2784 453 2785 2785 Answer: Question 27. 556 2011 2015 333 2016 2017 277 2018 2019 534 The equations of the lines shown are y = \(\frac{4}{3}\)x + 4 and y = \(\frac{4}{3}\)x – 8. m∠CAB = 60°, m∠DEF = 30° x = \(\frac { 55 }{ 2 } \) /Outlines 109 0 R 722 1736 1736 500 1737 1737 722 1738 1738 500 333 2030 2034 496 2035 2036 757 2037 2038 868 The coordinates of the vertices of ∆DEF are D(- 8, 5), E(- 5, 8), and F(- 1, 4), The coordinates of the vertices of ∆JKL are J(16, – 10), K(10, – 16), and L(2, – 8), ∠D ≅ ∠J. Is this possible? endstream << 1994 228 1995 1995 240 1996 1996 228 1997 1997 Therefore, the ratios \(\frac{18}{4}, \frac{27}{9}\) do not form a proportion. 390 990 990 624 991 991 285 992 992 569 >> >> The scale factor is \(\frac { 3 }{ 2 } \) In Exercises 5 and 6, find the value of x that makes ∆DEF ~ ∆XYZ. What do you observe? /ToUnicode 143 0 R using the three parallel lines theorem Prove the Converse of the Triangle Proportionality Theorem (Theorem 8.7). 1634 689 1635 1636 777 1637 1638 981 1639 1640 1113 1113 807 1114 1114 310 1115 1117 0 1118 722 2308 2309 500 2310 2310 389 2311 2311 358 Answer: Question 8. 666 55 55 610 56 56 722 57 57 666 453 453 500 454 454 389 455 455 556 456 If \(\frac { JK }{ KL } \) = \(\frac { NM }{ ML } \), then KM || JN 530 500 531 531 570 532 532 713 533 536 1707 878 1708 1708 821 1709 1709 878 1710 1710 What term does the description "two lines that intersect to form four congruent right angles" define? In Exercises 3 and 4, find the scale factor. According to the triangle angle bisector theorem \(\frac { CR }{ BR } \) = \(\frac { AC }{ AB } \). 1972 524 1973 1974 610 1975 1976 659 1977 1980 2111 2111 871 2112 2112 684 2113 2113 900 2114 2169 673 2170 2170 684 2171 2171 533 2172 2172 The leg c is the hypotenuse. If the cross product of two ratios is equal, then it forms a proportion. 277 1122 1122 268 1123 1125 277 1126 1126 552 536 496 537 537 491 538 538 277 539 539 473 473 689 474 474 666 475 475 799 476 ), question mark ( ? 212 722 213 213 277 214 223 333 224 224 993 994 419 995 995 483 996 996 419 997 132 0 obj >> x = \(\frac { 16 x 15 }{ 12 } \) = \(\frac { 240 }{ 12 } \) >> \(\frac { Perimeter of A }{ Perimeter of B } \) = \(\frac { Side length of A }{ Side length of B } \) \(\frac { PQ + QR + RS + SP }{ KL + LM + MN + NK } \) = \(\frac { PQ }{ KL } \) = \(\frac { QR }{ LM } \) = \(\frac { RS }{ MN } \) = \(\frac { SP }{ NK } \). Explanation: 0000105259 00000 n Answer: 542 2428 2428 382 2429 2437 542 2438 2438 382 36 37 610 38 38 666 39 39 722 40 DC = 8 2827 2827 277 2828 2828 500 2829 2829 277 2830 18y – 18 = 16y 2173 577 2174 2174 401 2175 2175 352 2176 2176 Longest sides: \(\frac { LN }{ ST } \) = \(\frac { 26 }{ 33 } \) = 48 = 2³ x 60 = 8 x 60 = 480 cubic in 137 500 138 139 759 140 140 979 141 142 has the lowest activation energy) step for this reaction is the The ΔH of the overall reaction would be step . Explanation: THOUGHT PROVOKING (D) 36 \(\frac{15}{21}, \frac{55}{77}\). List all pairs of congruent angles. 1929 1929 277 1930 1930 228 1931 1931 277 1932 Explain. 437 437 666 438 438 611 439 439 610 440 ∆ABC: BC = 18, AB = 15, AC = 12 2092 736 2093 2093 557 2094 2094 472 2095 2095 if and only if it has two pairs of parallel sides, a pair of adjacent angles whose noncommon sides form a straight angle, an organized, logical way of presenting a list of facts that leads to a conclusion, a pair of angles whose measures have a sum of 180∘, a proof given as specific statements and their supporting reasons in a table format, a pair of nonadjacent angles whose sides are opposite rays. 790 1109 1109 290 1110 1110 295 1111 1112 0 2830 500 2831 2831 556 2832 2832 474 2833 2833 /Type /XObject Question 19. 529 884 884 310 885 885 423 886 887 640 282 1233 1233 271 1234 1238 382 1239 1242 333 The triangles are similar. perimeter of smaller triangle = 32 610 2480 2480 500 2481 2481 277 2482 2482 722 785 785 500 786 786 556 787 790 233 791 << 2180 2180 501 2181 2181 409 2182 2182 495 2183 1381 666 1382 1382 500 1383 1383 666 1384 1384 trailer x = 4√2. /Subtype /CIDFontType2 /N 32 389 1063 1063 610 1064 1064 389 1065 1065 722 Answer: Use a diagram to show why there is no Side-Side-Angle Similarity Theorem. AC² = 64 /Iabc21 138 0 R fill in the word needed to make the resulting sentence true. Answer: endobj 370 2275 2275 179 2276 2278 229 2279 2279 357 392 777 393 393 556 394 394 277 395 395 636 1481 1481 758 1482 1482 636 1483 1483 517 443 235 235 610 236 236 500 237 238 674 FG = 4.8 The actual park is 800 yards long. ATTENDING TO PRECISION 500 2845 2845 228 2846 2846 833 2847 2848 556 <95873C0506EED3554467354814A4ACD8> ] 556 344 344 722 345 345 556 346 346 277 prove that m∠DEF = 90°. 1572 689 1573 1574 777 1575 1576 981 1577 1578 Explain your reasoning. Answer: f. Make a conjecture about the similarity of two triangles based on their corresponding side lengths. \(\frac { [latex]\overline{B D}\) }{ 30 } [/latex] = \(\frac { 16 }{ 40 } \) 684 2224 2224 533 2225 2225 882 2226 2226 716 Perimeter = kP In ∆RST, RS = 20, ST = 32, and m∠S = 16°. The ratios of side lengths are \(\frac { RQ }{ MN } \), \(\frac { QS }{ MP } \), \(\frac { RS }{ NP } \). Question 1. 713 2711 2715 0 2716 2716 915 2717 2718 883 1632 1632 500 1633 1633 722 1634 1634 500 1635 Explain. Answer: 0000001504 00000 n 28q + 36q = 576 3031 581 3032 3032 132 3033 3033 222 3034 3034 In Exercises 25 and 26, find the value of x for which \(\overline{P Q}\) || \(\overline{R S}\). Answer: 71 71 500 72 72 443 73 73 277 74 1853 1853 500 1854 1855 552 1856 1857 471 1858 This volume includes all thirteen books of Euclid's "Elements", is printed on premium acid-free paper, and follows the translation of Thomas Heath. 244 1259 1259 529 1260 1260 244 1261 1263 542 495 495 634 496 497 722 498 498 666 499 833 1609 1609 638 1610 1610 535 1611 1611 610 2772 484 2773 2773 824 2774 2774 604 2775 2775 Describe and correct the error in writing a similarity statement. 257 333 258 258 610 259 259 500 260 260 If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar because of the _____. 476 566 477 477 716 478 478 666 479 480 2031 2031 722 2032 2032 500 2033 2033 475 2034 Prove l || n 264 264 722 265 265 610 266 266 443 267 722 434 434 655 435 435 777 436 436 722 1870 1046 1871 1871 786 1872 1872 423 1873 1873 Therefore, perimeter = 6 + 8 + 10 + 12 + 10 = 46, Question 5. The slope of l = – \(\frac{3}{4}\) \(\frac{18}{4}, \frac{27}{9}\). 1463 1463 666 1464 1464 500 1465 1465 666 1466 178 585 179 180 333 181 182 222 183 183 Answer: Question 33. In Exercises 7 and 8, verify that ∆ABC ~ ∆DEF Find the scale factor of ∆ABC to ∆DEF. 556 1375 1375 277 1376 1376 228 1377 1377 277 Perimete of the park P = 2(1680 + 2400) 0000000012 00000 n 1050 1050 666 1051 1051 556 1052 1052 722 1053 722 419 419 500 420 420 722 421 421 500 In the diagram, PQRS is a square, and PLMS ~ LMRQ. (A) Lines l and n are parallel. Therefore, the ratios \(\frac{9}{24}, \frac{24}{64}\) form a proportion. When 2 figures are similar, then their corresponding angles are congruent and their corresponding lengths are proportional. 777 1936 1936 556 1937 1937 722 1938 1938 333 A child who is 58 inches tall is standing next to the woman in Example 3. Question 7. 718 666 719 719 556 720 720 666 721 721 0000080378 00000 n Question 1. 2087 2087 538 2088 2089 666 2090 2091 609 2092 >> So, \(\frac { AE }{ FK } \) = \(\frac { 2 }{ 3 } \) ∆FGH and ∆RQS MAKING AN ARGUMENT 1213 290 1214 1214 295 1215 1215 790 1216 1216 Question 41. The perimeter of JKLM : Perimeter of EFGH = 85 : 34. If a polygon is a triangle, then it has three sides. ∆DEF: EF = 12, DE = 10, DF = 8 The side lengths are not proportional. HOW DO YOU SEE IT? /Type /Font In Exercises 3 and 4, find the length of \(\overline{A B}\) . x = 24 x 9 3x = 180 976 976 545 977 977 500 978 978 450 979 The pairs of congruent angles are ∠K = ∠Q, ∠J = ∠P, ∠ L = ∠R 619 2253 2253 599 2254 2254 620 2255 2255 563 755 755 556 756 756 777 757 757 556 758 287 556 288 288 277 289 289 556 290 290 1843 1843 416 1844 1844 277 1845 1845 620 1846 1098 1098 498 1099 1100 531 1101 1104 855 1105 If the corresponding side lengths of two triangles are proportional, then the triangles are similar. x = 28, Explanation: 1931 1931 653 1932 1934 849 1935 1942 706 1943 2284 556 2285 2286 389 2287 2287 486 2288 2292 \(\overline{T V}\) is the angle bisector ATTENDING TO PRECISION The points P(2, 1), Q(4, 5), and R(7, 4) are the midpoints of the sides of a . /Length 716 161 162 556 163 163 277 164 164 583 165 Answer: 2960 2960 595 2961 2961 500 2962 2962 666 2963 (a) If the scale factor k = 2, then Answer: Area = k²A Answer: Question 24. 1112 1013 1013 944 1014 1014 777 1015 1015 443 Use dynamic geometry software. 524 1953 1954 394 1955 1956 496 1957 1958 277 The pairs of congruent angles are ∠K = ∠Q, ∠J = ∠P, ∠ L = ∠R What notation is used to represent the distance from point A to B? Two people leave points A and B at the same time. Question 4. /Fabc14 120 0 R as shown in the following figure. /H [ 1504 361 ] 666 169 170 556 171 171 565 172 173 666 688 594 595 1042 596 596 675 597 597 872 z = \(\frac { 3 }{ 4.5 } \) • 1.5 Find the ratios of the lengths of the sides of ∆A’B’C’ to the lengths of the corresponding sides of ∆ABC. The object and image are similar. 1345 1345 382 1346 1354 542 1355 1355 382 1356 132 134 500 135 135 350 136 136 522 137 endobj 1152 244 1153 1153 714 1154 1154 244 1155 1155 /PageMode /UseNone Decide whether the hexagons in Tile Design 2 are similar. (c) Perimeter is 7 ft, area is 2 sq ft, Explanation: Prove ∆ABC ~ ∆DEF x = 216. The distance DA between Earth and the Sun is 93,00,000 miles. 500 1057 1058 228 1059 1059 566 1060 1060 382 \(\frac { x }{ 18 } \) = \(\frac { 2 }{ 3 } \) 2253 2253 374 2254 2254 600 2255 2255 544 2256 1779 1779 722 1780 1780 500 1781 1781 722 1782 1326 542 1327 1327 382 1328 1332 542 1333 1333 \(\frac { 2 }{ 800.3 } \) = \(\frac { 1.4 }{ EF } \) 932 1579 1580 901 1581 1582 576 1583 1584 500 677 582 582 833 583 585 722 586 586 610 Answer: Two coplanar lines that never intersect are called parallel lines. 953 953 722 954 954 779 955 955 589 956 2792 295 2793 2793 594 2794 2795 394 2796 2796 Alternate Interior Angles Theorem (Thm. 666 1776 1776 500 1777 1777 722 1778 1778 500 858 858 714 859 859 310 860 861 714 862 422 422 722 423 423 500 424 424 722 425 710 710 438 711 714 619 715 717 478 718 /Filter /FlateDecode 1702 500 1703 1703 610 1704 1704 500 1705 1705 556 762 762 777 763 763 556 764 764 777 A cellular telephone tower casts a shadow that is 72 feet long, while a nearby tree that is 27 feet tall casts a shadow that is 6 feet long. Found insideThen we describe the essential factors that are useful in knowing the meaning of a sentence. ... Ogden and Richard proposed a triangle showing the relations between a word as a symbol, its referent in the real world and the ... The scale factor k = \(\frac { CP }{ CP’ } \) endobj 274 274 322 275 275 666 276 276 500 277 2335 2335 352 2336 2337 443 2338 2338 389 2339 What are the perimeter and area of the actual park? The two gazebos shown are similar pentagons. 1019 610 1020 1020 500 1021 1021 889 1022 1022 2926 0 2927 2934 576 2935 2942 240 2943 2950 1932 228 1933 1933 777 1934 1934 556 1935 1935 Answer: 435 277 436 436 443 437 437 277 438 438 916 386 387 750 388 388 531 389 389 656 Question 39. \(\frac { 6 }{ 72 } \) = \(\frac { 27 }{ x } \) Answer: So, \(\frac { perimeter of patio }{ perimeter of backyard } \) = \(\frac { 2 }{ 5 } \) Answer: Question 4. 963 963 756 964 964 277 965 965 333 966 THOUGHT PROVOKING Explain your reasoning. 579 591 0 592 592 259 593 593 0 594 389 639 641 277 642 642 679 643 643 711 Answer: Question 32. 0000001866 00000 n scale factor = \(\frac { EF }{ JK } \) =\(\frac { 8 }{ 20 } \) 277 80 80 722 81 84 500 85 86 389 Is the converse true? 2741 350 2742 2742 477 2743 2743 299 2744 2749 Find the length of \(\overline{F G}\). 523 523 610 524 524 703 525 525 723 526 The ratios are equal. << = 4 x 16 = 64 361 722 362 362 556 363 363 722 364 364 2486 556 2487 2487 389 2488 2488 443 2489 2489 << In the structure illustrating the bonding in ethene, C2H4, the two arrows point to what type of bond or bonds. 2610 2611 374 2612 2612 376 2613 2613 604 2614 Can you show that ∆DEF ∆JKL by using the AA Similarity Theorem (Theorem 8.3)? If so, do so by listing the congruent corresponding angles and writing a similarity transformation that maps ∆DEF to ∆JKL. 1722 443 1723 1723 610 1724 1724 443 1725 1725 shortest sides: \(\frac { 3 }{ 4 } \) Answer: Determine whether there is enough information to prove that the triangles are congruent. Prove Ceva’s Theorem: If P is any point inside ∆ABC, then \(\frac{A Y}{Y C} \cdot \frac{C X}{X B} \cdot \frac{B Z}{Z A}\) = 1 Explain how you know that the yellow triangle is the midsegment triangle of the red triangle in the pattern of floor tiles shown. 16 333 17 18 277 19 28 556 29 30 2066 2067 751 2068 2068 708 2069 2071 333 2072 = 4² x 12 = 16 x 12 = 192, Question 2. 2012 869 2013 2019 524 2020 2024 610 2025 2029 Compare the perimeters of ∆A’B’C and ∆ABC. 2869 334 2870 2870 372 2871 2871 334 2872 2872 413 2096 2097 573 2098 2098 500 2099 2099 228 821 1711 1711 777 1712 1713 333 1714 1788 0 Answer: = 130 ft Answer: c. Change ∆ABC and repeat parts (a) and (b) several times. Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion stream Include a diagram in your answer. Without using corresponding lengths in similar polygons. /Fabc9 119 0 R Which of the three beveled pieces, if any, are similar? /W [ 1 1 0 2 3 250 4 4 333 5 943 1460 1460 722 1461 1461 943 1462 1462 722 556 1895 1895 666 1896 1896 556 1898 1898 889 777 2073 2073 556 2074 2074 722 2075 2075 500 998 461 999 999 383 1000 1000 323 1001 1001 556 272 272 291 273 273 556 274 274 368 556 1756 1756 277 1757 1757 556 1758 1758 277 Scale factor = \(\frac { 2 }{ 3 } \) 1277 1277 382 1278 1286 542 1287 1287 382 1288 \(\frac { BC }{ GH } \) = \(\frac { 2 }{ 3 } \) 1942 556 1943 1943 722 1944 1944 556 1945 1945 BIM Geometry Book Solutions are available for all chapters along with Chapter 8 Similarity on our website. Therefore, the ratios \(\frac{26}{8}, \frac{39}{12}\) form a proportion. So ∆SRT ~ ∆PNQ. cross multiply the fractions shorter sides: \(\frac { 6 }{ 15 } \) = \(\frac { 2 }{ 5 } \) \(\frac { DB }{ BE } \) ≠ \(\frac { CA }{ AE } \) Question 20. (Only the first quadrant is shown, since the triangle is located in the first quadrant.) 1829 1829 833 1830 1830 666 1831 1831 833 1832 cross multiply 505 2155 2155 500 2156 2156 472 2157 2158 520 2521 333 2522 2522 277 2523 2526 333 2527 2528 546 405 547 547 458 548 548 439 549 549 m∠NRQ = ___________ 3x = 264 738 277 739 739 228 740 740 277 741 741 This picture shows a group of children and adults. Explain your reasoning. 1860 610 1861 1862 659 1863 1866 610 1867 1872 /ImageC /ID [ Answer: Question 18. 2(21 – p) = p 90 666 91 92 443 93 93 389 94 94 Answer: 567 664 568 568 672 569 569 722 570 570

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