IM 8.2.9 Lesson: Side Length Quotients in Similar Triangles
Triangle [math]A[/math] has side lengths 2, 3, and 4. Triangle [math]B[/math] has side lengths 4, 5, and 6. Is Triangle [math]A[/math] similar to Triangle [math]B[/math]?
Triangle [math]ABC[/math] is similar to triangles [math]DEF[/math], [math]GHI[/math], and [math]JKL[/math]. The scale factors for the dilations that show triangle [math]ABC[/math] is similar to each triangle are in the table.[br][br][img]data:image/png;base64,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[/img][br][br] Find the side lengths of triangles [math]DEF[/math], [math]GHI[/math], and [math]JKL[/math]. Record them in the table.
Your teacher will assign you one of the three columns. For all four triangles, find the quotient of the triangle side lengths assigned to you and record it in the table. What do you notice about the quotients?
Compare your results with your partners’ and complete your table.
Triangles ABC and DEF are similar.
[img]data:image/png;base64,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[/img][br] Explain why [math]\frac{AB}{BC}=\frac{DE}{EF}[/math].[br]
Triangles ABC, EFD, and GHI are all similar. The side lengths of the triangles all have the same units. Find the unknown side lengths.
IM 8.2.9 Practice: Side Length Quotients in Similar Triangles
These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale.
Here is triangle ABC. Triangle XYZ is similar to ABC with scale factor 1/4. Draw what triangle XYZ might look like.
How do the angle measures of triangle [math]XYZ[/math] compare to triangle [math]ABC[/math]? Explain how you know.
What are the side lengths of triangle [math]XYZ[/math]?
For triangle [math]XYZ[/math], calculate (long side) [math]\div[/math] (medium side), and compare to triangle [math]ABC[/math].
The two triangles shown are similar.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO4AAAFeCAYAAACCUyPjAAAgAElEQVR4Ae2dh3cUR9b2379kbSMUkYRAIkqgaDImOOB1AJyWDCKKnAXO67BO3zoBJoMQAhQQmRe8tve1wQgQwZIQICQZUDAKpL3fucVKVphuTc9U91T3PHWODjNV3RV+NQ/dXX3r3v8hJBAAAdsR+B/b9RgdBgEQIAgXPwIQsCEBCNeGk4YugwCEi98ACNiQAIRrw0lDl0EAwsVvAARsSADCteGkocvOIlBXV0drVqfThnXr3R4YhOs2KhwIAuYQyN67j7pFRNLC+QvcbgDCdRsVDgQB+QQqKyqpf2wcjRz+FJWUlLjdAITrNiocCAJyCTQ2NNDkiZOoa3gEZWZkGKocwjWECweDgBwCDx48oB3btgvRzpszl/g510iCcI3QwrEgIInA1dJSGjZ4CCXE9aOK8nLDtUK4hpHhBBDwjsDDhw9p2ZKlFBoUTAcPHPSoMgjXI2w4CQQ8J7BndxaFBAbRgrT59Mcff3hUEYTrETacBAKeESg8f56S4hMooV9/Kjx33rNKiLA7yGNyOBEEDBK4c+cOzUqdSYFPdCK+6nqTcMX1hh7OBQEDBLIyMykqPELcIvNzrjcJwvWGHs4FATcJsKFFYv94GjViJF2/ds3Ns7QPg3C12aAEBKQQ4KvrhDf+RpFhXYivujIShCuDIuoAAQ0CbGiRsWMnRYSGiedbfs6VkSBcGRRRBwhoECguKqYRw4ZTXJ++dMWALbJGdc3ZEG4zCnwAAfkEVi5fQUEBnenQwUNSK4dwpeJEZSDwJwHerhcaGERLFi2m+vr6PwskfIJwJUBEFSDQlgAbWvTrG0sDklOo8Hxh22Kvv0O4XiNEBSDQmgDv9EmdPoMCHntcLEz95z//aX2AhG8QrgSIqAIEWhLIytwtDC1mTJ1G3hpatKy35WcItyUNfAYBLwncvHmTBg8YSE8NHUY3ym54WZv26RCuNhuUgIAhAnx1nTp5itgcz1ddM26RmzoE4TaRwL8g4AWBRx4ttlFI50BKmzvPsEcLo01DuEaJ4XgQcEHg0sWLwqNFbO8+xEYXZicI12zCqN8vCCxdvISCOwfS0cNHLBkvhGsJZjTiZALHjx4THi0WL1xE9+7ds2SoEK4lmNGIUwlcvnSJ+vbsJVaSz587Z9kwIVzLUKMhpxHgnT4zZ6RSp788Rtu2bDHtna0rbhCuKyrIAwE3COzcvkO8+pkyabKlouWuQbhuTBAOAYG2BG7dukVDBg6i4UOGEn+2OkG4VhNHe7YnwIYWfJXlQF252dk+GQ+E6xPsaNSuBNgaKjNjl3iu5dAhsrfrucsFwnWXFI4DASK6eOGCMLToFR1DbHThqwTh+oo82rUdAX5Hu2LZcrE5fn9unk/7D+H6FD8atxMBtopi6yi2kvJ1gnB9PQNo3xYEfrt8mdgOmSPs+fIWuQkWhNtEAv+CgAYBDszF2/V458+ObduIdwL5OkG4vp4BtK88ATa0YGfmr7/6muWGFlpwIFwtMsgHASLi0CFsZDEw5UmqrKxUhgmEq8xUoCOqEWBDC94U3z2yK+Xs26dU9yBcpaYDnVGJwN6sPcLQgsXrK0MLLR4QrhYZ5Ps1AfaFzD6R2TeyCqvIbScDwm1LBN/9ngBfXTn6AEch4GgEKiYIV8VZQZ98SuDkiZMU2CmA2KOFqgnCVXVm0C+fELh29SrFx8bR0EGDiY0uVE0Qrqozg35ZToA9WsyYNp3CQ0Jp6+YtShhaaEGAcLXIIN/vCGzfuk0EoH79lVfp7t27So8fwlV6etA5qwhcv3ZNGFqkJCULowur2vW0HQjXU3I4zzEE2NBiQdp8YWiRn7ffFuOCcG0xTeikmQT27M6iwCc6ie16DfUNZjYlrW4IVxpKVGRHAuwXOSk+QawkXyy8YJshQLi2mSp0VDYBXkVeuviRoQUvTNkpQbh2mi30VSoB9mgRHhpG8+el0f3796XWbXZlEK7ZhFG/kgQ46HRCXD/h0eJqaamSfdTrFISrRwdljiTAt8hNAah3bNuutKGF1gRAuFpkkO9YApu+20hdgkNo8sRJ1Nhgj1XktpMB4bYlgu+OJsC3xezRom+v3lR+o9y2Y4VwbTt16LhRAhyFgP0ic+iQ/bm5Rk9X6ngIV6npQGfMJMBxfsKCgmnZkqVkF0MLLR4QrhYZ5DuKAG/R49vj5IREJT1aGIUN4RolhuNtR+CP2lphi8xRCLZt2Wq7/rvqMITrigryHEWA4/xEdgkXhhaqb9dzFzyE6y4pHGdLAtXV1ZTYP174Ra4ot+8qclv4EG5bIvjuGALs9C11+gyKiogkNrTg7XtOSRCuU2YS42hHYMumzRQSGETTpkwljv/jpAThOmk2MZZmAk2GFl3DI6jsellzvlM+QLhOmUmMo5lAk6FFVHgEHcw/0JzvpA8QrpNmE2MRBPJycoSnxpXLVxBHkXdignCdOKt+PCb2i9y9axSlJCYRe7dwaoJwnTqzfjiu2tpa8a6WoxBsWLfe0QQgXEdPr38NLmdftvDUOHNGqu1tkTuaOQi3I0IotwUBdj3Ddsjs1YKNLpyeIFynz7AfjK/J0IK362VlZhKvKjs9QbhOn2E/GN/GDd9R58efoNkzZxE/5/pDgnD9YZYdPMYrJSXCDpktpNgBnL8kCNdfZtqB4+Rb4vRVqykirAvl5djbo4XR6YFwjRLD8coQOHLoELFJI3u08Ifn2pbgIdyWNPDZNgQqyivErp8BySmONrTQmhAIV4sM8pUlwAtQvBDFC1K8MOWPCcL1x1m38Zj5lphf+fCrH95ry6+C/DFBuP446zYec01NDQ1IShZeLerr6mw8Eu+6DuF6xw9nW0iA/UVxgC5ekOKYtv6cIFx/nn2bjZ1vkYMCOtOcWbOpxg/MGvWmB8LVo4MyZQgUFxXRiGHDqVtkVyr6rUiZfvmqIxCur8ijXbcJ8GZ43hQfHhJKvEkeiQjCxa9AeQLsfobd0CxIm+93hhZakwPhapFBvhIEOKJej+7RNGTgILpQWKhEn1ToBISrwiygDy4JNG3X49AhG9atw9W2BSUItwUMfFSHADsvz8zYJTxacABqjiKP9CcBCPdPFvikEIGKigoaNngwRUV0pcrKSoV6pkZXIFw15gG9aEHgwYMHYsdPp788RkMHDW5Rgo9NBCDcJhL4VxkCu3ftIvbUGPhEJwhXY1YgXA0wyPYNgUsXL9KwwUOEocWoESMhXI1pgHA1wCDbegKNjY20asVK4lVkDtiVOm06hKsxDRCuBhhkW0+APVpEd40StsgcXQ/C1Z4DCFebDUosJFBZUUkJ/fo3G1rw6x8IV3sCIFxtNiixiADbIk+fOo1CA4No/bffilYhXH34EK4+H5SaTIBf/XC0eN5jO3XylGZDCwhXHzyEq88HpSYT4ADUvIrMoUNa+kWGcPXBQ7j6fFBqIgE2a2TXqqFBwXTwwMFWLUG4rXC0+wLhtkOCDKsI8N5ajkDA2/V4FbllgnBb0mj/GcJtzwQ5FhDgoNO8VY9XkgvPnW/XIoTbDkmrDAi3FQ58sYIAG1qwR4uAxx6njB07XTYJ4brE0pwJ4TajwAerCOTn7Rfb9dipOT/nukoQrisqf+ZBuH+ywCcLCLChRUpSMg0fMpR+u3xZs0UIVxONKIBw9fmgVCIBvrpOeONv1CU4hDZv3KRbM4SriwfO4vTxoFQWATa04OfZiNAwmjRhQrtV5LbtQLhtibT+jituax74ZhKB4qJi4Rc5rk9ft/wiQ7j6EwHh6vNBqSQCvIrMUQgOHTzkVo0Qrj4mCFefD0olEDh+9JgwtOC4P+5G14Nw9cFDuPp8UOolAfZowdH1OAB14Xn3/SJDuPrgIVx9Pij1gkBDfQMtXrhIBKDmhSmObetugnD1SUG4+nxQ6gWBA/vzhUcL9ousZWihVT2Eq0XmUT6Eq88HpR4SuHnzpjCyYHvk4uJiw7VAuPrIIFx9Pij1gABfXXlTPL+z3bJpk+GrLTcJ4eqDh3D1+aDUIAEWLftF5u16bCVVW1trsIZHh0O4+tggXH0+KDVIoMkvcmzvPrq2yB1VC+HqE4Jw9fmg1CCBpYuXCL/IRw8fMXhm68Mh3NY82n6DcNsSwXePCZw8cVLcIvMrIPbc6E2CcPXpQbj6fFDqJoHioiJKTkikwQMG0vlz59w8S/swCFebDZdAuPp8UOoGATZjXLRgoTC02LZli0eryG2bgXDbEmn9HcJtzQPfPCBwMD9feLQY9/JYKaLlLkC4+hMB4erzQWkHBG7dutVsaHHt2rUOjna/GMLVZwXh6vNBqQ4Bfmc7ZdJkEYVg5/YdhmyRdaoVRRCuPiEIV58PSjUI8IaBzIxdxFHjWbxt/SJrnOZ2NoSrjwrC1eeDUg0CFy9cEKFDekXHUOH59n6RNU5zOxvC1UcF4erzQakGgRXLlovoevtz8zSO8C4bwtXnB+Hq80GpCwIFZwqEG5qF8xe4KJWTBeHqc4Rw9fmgtA0BdvrWr2+suE1mu2SzEoSrTxbC1eeD0hYE6urqKG3uPLEgtWPbNmKXq2YlCFefLISrzwelLQjkZmdTVHgEvTDmeWmGFi2qb/URwm2Fo90XCLcdEmS4IsChQ0aPHEXJiUlUUV7h6hCpeRCuPk4IV58PSonE1ZVvkbuGRxAbWliRZAqX3znX1NRQdXW1FV23pA0I1xLM9m5kb9aeZkMLFpQVSZZwf/n5Zxo1YqTYAMHGIvFx/ehf339vxRBMbQPCNRWv/SvniHq8Va9vz1505tczlg3IW+HebWykb776msKCgmnsiy/Rxx9+SJ9/+hktW7KUCs5YNw6zgEG4ZpF1QL28GX7JosXC0CJ77z5LR+StcH/84Qfq0T2a1qxOp6qqqlZ9N+oqttXJinyBcBWZCBW7cfrUaQrsFCCcmlvdP2+FO2fWbHGnwK+wnJggXCfOqoQxXb9+nRL7x9PQQYO9cvrmaVe8Ee7du3cpOqobvfv2O6a+a/Z0bDLOg3BlUHRYHezRggN0BQd0pq2bt/jkx++NcNmii/vObmKdmiBcp86sF+PK3rv3v4YWY4ivXr5I3giXV5L51dXRw4d90XVL2oRwLcFsn0Zu3LhBzz39DHEA6rLrZT7ruDfCPXf2LIV0DqRdOzN81n+zG4ZwzSZso/p5tXVB2nxxtc3KzPRpz70RbmNjIyUnJtKLzz/f/HzOxhd5ubk+HZPMxiFcmTRtXtee3VkU+EQnmpU6Uzhr8+VwvBEu93t/Xh5FRUSK+EV82xzZJVz4fPblmGS2DeHKpGnjui5fukRJ8QkUHxunhIGCt8JlM0e+ZWbDi7Xp6fTlF1/Q2YICG89Q665DuK15+OW3xoYGWrr4kaHF9q3blGDgrXCVGISJnYBwTYRrl6p/+vEnCg8NE6+A7t+/r0S3IVz9aYBw9fk4vvTWzVuUkphEA1OepCslJcqMF8LVnwoIV5+Po0vZHHDenLnUJTiEdmzb7hNDCy3AEK4WmUf5EK4+H0eXZmZkCEOF8WPHEj/nqpQgXP3ZgHD1+Ti29GppKT09ajT17tHTp4YWWoAhXC0yj/IhXH0+jizlVyXsF5nfb6pqzwvh6v/0IFx9Po4sZadvvMGct77JDh0iCxiEq08SwtXn47jS0iulFNunLyXE9aMCCz1aGAUJ4eoTg3D1+TiqlFeR2RY5uHMgbduyVWp0PdmgIFx9ohCuPh9Hlf7vsePCZpf32vpqu567QCFcfVIQrj4fx5Sye9ImQ4uK8nLlxwXh6k8RhKvPxxGlDfUN4hY5IjRMGFrYwVkahKv/04Nw9fk4opRf+USEdaHXxr+i7CpyW9AQblsirb9DuK15OO5bk6EF70e9du2abcYH4epPFYSrz8fWpWxosTZ9jbjaZuzYaauxQLj60wXh6vOxdWleTg6Fh4SK51v23GinBOHqzxaEq8/HtqXXrl6l7l2jxEoye4KwW4Jw9WcMwtXnY8tSNrTgd7UchWDDuvVKG1poAYZwtcg8yodw9fnYsvTI4cPUPbIrzZyRSvwqyI4JwtWfNQhXn4/tSh88eEADkpKFLbKd48FCuPo/PQhXn4+tStmf8NLFS4RLUg5AzavKdk0Qrv7MQbj6fGxVymINDQyiSX+bQLW1tbbqe9vOQrhtibT+DuG25mHbb+zobcSw4cLpt50MLbSAQ7haZB7lQ7j6fGxRyrfE6atWCxerqnq0MAoSwtUnBuHq87FF6ZFDh4QbmrQ5c4mfc52QIFz9WYRw9fkoX1pRXiFi5AxIThEhN5TvsJsdhHD1QUG4+nyULm1oaKC0uXMp4LHH6ZuvvlZ2FZkDTedm54hAXByMy52/rN27acwzz9LQQYOVngNfdQ7C9RV5Ce3m5+2nbhGRlDp9Bqlsi/zmmjX07tvvUM6+bLf/MjN2iTi9EK7rHwqE65qL8rlsaDF4wEBK7B9P9XV1Svd3zerVdOTwEUN9xK2yPi4IV5+PkqXsL4oNLThQF8e0VT1BuPJnCMKVz9T0GjlaPAegnjxxEtVUV5venrcNQLjeEmx/PoTbnonSOcVFRcLQgl2sXrp4Sem+NnUOwm0iIe9fCFceS9NrunfvHr25Zq2IQsDmjXZJEK78mYJw5TM1rcaD+QcoKjxCeLSw0wYCCFf+TwLClc/UlBrLb5RTj+7RNGTgILpQWGhKG2ZVCuHKJwvhymcqvcaG+nrxrpafazesW6esoYXWwCFcLTKe50O4nrOz5Ey+Jc7LzRUeLXgVmd9v2i1BuPJnDMKVz1RqjRwGc9RTI4RHi8rKSql1W1UZhCufNIQrn6m0Gtk6irfrcSxbNhe0a4Jw5c8chCufqbQaOQB1UEBnmjp5ii0MLbQGDuFqkfE8H8L1nJ2pZ14sLBQryLzzZ9CAgfTKuHG2/esfGyeMRoyMYexLL1PvmJ7YHaTxK4NwNcD4Mps3w69asVIEoO4ZHUP+/PfSX1/w5VQo2zaEq+DUsEeL6K5RNCt1JhX/VkQlRcV++3f9+nUFZ8j3XYJwfT8HrXpQWVFJCf3629LQotVA8MVUAhCuqXiNVX7//n2aPnWacLG6/ttvjZ2Mo/2KAISryHSzocX+3Fxhizzh9Tds7xdZEayO7QaEq8jU/v77782GFjfKbijSK3RDVQIQrgIz8/DhQ1qzOl04Mz944KACPUIXVCcA4SowQxyAmjcQsNM3NnFEAoGOCEC4HREyufzypUtiBblXTA868+sZk1tD9U4hAOH6cCbZ0GLl8hXCL/KWTZt92BM0bTcCEK4PZ4wDUEdHdRO2yPyciwQC7hKAcN0lJfk4NrRISUqm4UOG0m+XL0uu3ZzqCs6cEdZcBWcKzGkAtbpNAMJ1G5W8A/nqOuGNv1GX4BDavHGTvIpNriljxw4K6hRAdo50bzIiy6qHcC1D/aghFm323n0iavykCRNss4rMe4PfWvsmJScmWUwMzbkiAOG6omJiXtn1Mnp29NMU16cvFf1WZGJLcqvmhbTxY8fSlEmT5VaM2jwiAOF6hM3zk95+8y2xOf7QwUOeV2LBmefOnhWBuj7+8EMqLS0Vvq769Y2lLz773ILW0URHBCDcjghJLD9+9JiwjkqdPl3Z6Hq1NTW0Nn0NxUR1E5vYnxo6jFISk+hgfr54Jj+Qny+RCKrylACE6yk5g+dxjNgBScnE3iBUNrR4a+1a4b/5q3/+kyorKqiqqoq2b91KMd26U/++sfTr6dMGR47DzSAA4ZpBtU2dDfUNtHjhIur8+BPEhhaqRiFgR+vBAZ1p/rx5xEGzmxKHPun0l8dEvNqysrKmbPzrQwIQrgXwD+zPFx4t2C+yyoYWy5Ysoa7hEXT4UOvnb16YYuGy07qWgrYAHZrQIADhaoCRlX3z5k1hZMGhQ4qLi2VVK70eFuSIYcPFajffHrdMp0+dEncL77/7XstsfPYhAQjXRPh8S8xXqYjQMNqyaZPSV9sbN25QUnwCPTN6dDsif3/vfbGotjdrT7syZPiGAIRrEncROiQnR/zg2UqqtrbWpJbkVFt2/Tol9o8XwbJb1sh3CQNTnqTwkFDiBTYkNQhAuCbNw7WrV+m5Z56lPj160oXz6kfX41t6fu0zbPCQ5ufYuro6WrZkqXgNFNu7D929e9ckWqjWKAEI1ygxN4/nd6G8Of7o4SNunuHbw/gOgRenuM8zpk2jzz/9VDzzLkhLowEpKbCY8u30tGsdwm2HxPuMkydOilvkObNmE79KsUvizQP8TJ6ckEiDBwykLz77jNivMZs54vlWrVmEcCXPR3FRkfjh8/Pi6V9OSa7d/Or4dRUbXsCFjvmsvWkBwvWGXptz6+vradGCheLVCQeg5h01SCBgBgEIVyJVtuftHtmVxr08VulXPxKHjKp8RADClQS+uqqaRo8cRU8mp9DV0quSakU1IOCaAITrmouhXH4u5AUcNhfcuX2HsrbIhgaFg5UmAOF6OT38GoU9WrAtL4sXizpeAsXpbhGAcN3CpH1QSXEJPT1qNPWKjqHC8+e1D0QJCEgkAOF6CZP9MIUGBtH+3Dwva8LpIOA+AQjXfVbtjjx+7JjwejhzRmq7MmSAgJkEIFwP6bItckJcP2EimJWZ6WEtOA0EPCMA4XrAjY3v0+bOEwtSYUHBlLMv24NacAoIeE4AwvWAXW52tghAndAvniBcDwDiFK8JQLgGEXLoEDa0YMfgWZm7IVyD/HC4HAIQrgGO/M6Wb5GbDC3+dfJ7CNcAPxwqjwCEa4Alv/JpMrS4c+cOQbgG4OFQqQQgXDdxXim5QqNGjKS+PXs1+0WGcN2Eh8OkE4Bw3UDKm+HXrF4tbovZvLEpQbhNJPCv1QQgXDeInz51mgI7BdDc2XNaHQ3htsKBLxYSgHA7gM2uW9ibxZNJyXS2oHVAZwi3A3goNo0AhKuDlj1azJ+XJsJyrPvmW7p//36royHcVjjwxUICEK4O7Oy9e4WhxQtjxrh0TQrh6sBDkakEIFwNvOzZ/7mnnxEhOTgYtasE4bqigjwrCEC4LiizocWKZcuFocWObdtdHPEoC8LVRIMCkwlAuC4A5+XkUOATnWhW6kwRid3FISILwtUig3yzCUC4bQizRwsOwxEfG0cFZ860KW39FcJtzQPfrCMA4bZg3djQQGtWpwtDi+1bt7Uocf0RwnXNBbnmE4BwWzD+6cefKCKsC7FHi7avfloc1vwRwm1GgQ8WE4Bw/wv81s1bIlodx80pdDO6HoRr8a8VzTUTgHCJiA0tFi9cJG6Rv/nqa7cDdUG4zb8jfLCYAIRLRJkZGeLVz/ixY6m+rs7tKYBw3UaFAyUT8HvhXi0tFX6Re/foSVqGFlrMIVwtMsg3m4BfC7elocXuXbsMs4ZwDSPDCZII+LVwD+YfEM+1HIDak9AhEK6kXyGqMUzAb4V77do1GpCcInwjF/yqb2ihRdVb4d69e5dqqmvo9u3bxC5f+Q4ACQTcIeCXwm34r6EFhw7ZsG69x4LxRri/nj5Na9PX0Et/fYFGjxxJs1JTad+evcRGIEgg0BEBvxTu/x47TlERkcIWma96niZPhft///43JcUn0KAnB9DGDRuItw+mzZ1L0V2jaPPGjZ52B+f5EQG/E25NTU2zoUVxUbFXU+2JcBsbGmnZkiXUo1t3unXrVnP7/B/Iu2+/TTHduovb5+YCfAABFwT8SrgN9Q20IG0+RYSG0Xfr17tl1uiCWXOWJ8ItLy8XDtXZJrptYtc47EXy6y+/bFuE7yDQioBfCZdf+bAt8mvjX6HamppWIDz54olw2c0r+7DatTOjXZNVVVXCt9Ubr73ergwZINCSgN8It8nQIrJLOPGKsozkiXBvlJXR8CFD6f1332vXhYqKCiFq3laIBAJ6BPxCuPyahVdw+WqbsWOnHg9DZZ4IlyMgzJ83Twj0/Llz9ODBA9EmP+9+9sknFB4SKq66hjqCg/2OgF8Ilw0tWBD8fMsbCmQlT4TLbfOrIN6oz3+vv/IqTZk0iUYOf4qmTp5CvWN6EDunQwIBPQKOFy7bH/eLjRMryefOntVjYbjMU+FyQ9VVVfTpP/5BkydOpBnTptOe3VlUUlIiDEL41RASCOgRcLRw2Rpp5fIVImq8N4YWWgC9Ea6rOk+eOCHe5e7Y1rH3DVfnI89/CDhauEcOHxbvRfkWlF8FyU4yhcvxif7+3vviVplXl5FAQI+AY4XLiz4DkpKpX99Yw9v19IC1LJMp3NO/nBJX23989FHLJvAZBFwScKRwGxsbaeniJc2GFk0rty4JeJHpqXB5BTk3O5uOHDpEe3bvppXLl4s7g9kzZxGutl5MiB+d6kjhZmXupi7BIcSGDLzzxqzkqXBLr1wRmwv4fS6vJqdOn0Hbt26lyooKs7qKeh1GwHHCZQOHEcOGU0hgkDRDC60591S4WvUhHwTcJeAo4bKhBVskhYeGkSceLdyF1nQchNtEAv9aTcBRwhXb9cIjKG3OXOLnXLMThGs2YdSvRcAxwq2srKS+vXpT/9g4km1ooQUPwtUig3yzCThCuOzRYvnSZRTUKYA+/ccnHnu0MAobwjVKDMfLIuAI4R4+eIh6xfSg1199zSOnb57ChHA9JYfzvCVge+HyO9rBAwZS/76x9Pvvv3vLw9D5EK4hXDhYIgFbC5fdvbChBa8ib928xbJb5Cb+EG4TCfxrNQFbCzcrM1MEoJ48cZKphhZakwLhapFBvtkEbCvca1evCkOL4M6BdOniJbM5uawfwnWJBZkWELCtcD/64EMRhWDn9h0WYHLdBITrmgtyzSdgS+H++8efKDqqG7FR/sOHD82npNEChKsBBtmmE7CdcCsrKqlnTA/iANQXCgulAOKVafb/9PP//WzojzfnhwUFU86+bCn9QCUg4C4BWwm3ob6eFi1YSAGPPU5ffPa5tFXkq6VXha/jtLnzyMjfq+PGQ7ju/tJwnFQCthEubyDIy82lntEx9Mq48VINLVi406ZMNQwWt8qGkeEESToEb4oAAAgvSURBVARsI1wOgznqqRHCo4XsfasQrqRfE6qxjIAthMvPoOmrVovb0u1b5TtSg3At+72hIUkEbCFcdvMSFNBZ+B1uGShLEgOCcGWRRD1WEVBeuBw6hD1aRIVH0BkPA1B3BBPC7YgQylUjoLRw79+/T++9867wi2ymoQWEq9rPEv3piIDSwuVVWza0mDNrtqmGFhBuRz8TlKtGQFnh8ha9pIREEQBLlqGFFnwIV4sM8lUloKRw+RZ5/rw04dHis08+NZ0dhGs6YjQgmYBywmVDi/25udSjezS99MKLVCMhAHVHzCDcjgihXDUCygn35s2b9NzTz1Bs7z5UXFRsCS8I1xLMaEQiAaWEyzt91qxOF87MOeykVQnCtYo02pFFQCnh5mbnUGCnAHHF/f7ECeFmlV2tmv3HMXzGvTzWcDvsLge7g2T9FFGPEQLKCLekuEQ4fev0l8eoe2RXEYg6JTHJkn8T4vpRRFgXw23x7TyEa+TnhmNlEVBCuBwblg0teLve+LFjae7s2bb5W7RgAf16+rSs+UA9IOAWASWE+9MPP4pVZA5A7UuPFm4Rw0EgoAABnwuXNw1wuEm+Lb5QeEEBJOgCCKhPwKfC5avrzBmpFNI5kL78f/9UnxZ6CAKKEPCZcFm02Xv3iYUoXtG1wtBCEeboBgh4TcBnwi27XkbPjn5aRNj77fJlrweCCkDAnwj4TLhvv/mW2By/N2uPP/HGWEFACgGfCPf40WPCOip1+nSqqa6WMhBUAgL+RMBy4ZZeuSIMLeL69KVffv7Zn1hjrCAgjYClwm1sbBS2yJ0ff4K2bNoszS+yNBqoCARsQsBS4Z48cYJiunUnjq4HQwub/ELQTSUJWCbc27du08jhT9GTySlUXGzNdj0liaNTICCBgCXC5c3x8+bMEQb5X3/5Fa62EiYOVfg3AdOFK0KH5ORQZJfwRx4tqmu8Jl5bUyNi4nJcXK2/Wzdv6rZTU11D/P7Y1fl/1NbqnotCEPA1AdOFywGon3vmWeoVHUNnCwqkjHffnj0UFRGp+/fRBx/otsV7aXvF9HBZR86+fbrnohAEfE3AdOG+9847FBoYRLt2Zkgba3V1team9927MikyrAsdPnRIt71PPv6YortGuayHr8ZIIKAyAVOFe/LESWFowX6R6+rqLOHArm94Eay+vl6zPV7Rfuett4X7V82DUAACChMwTbhsaMHBpxP7x9PpX05ZguDGjRvUp2cv+vrLL3UXwBobGmnJosU05tnnLOkXGgEB2QRMES4LY83q1cSGFhvWrSOOtmdFWrViJcXHxVHh+fO6zd25c4dmz5xFkyZM1D0OhSCgKgFThPv9yZPC0IK361llaHGlpIQiQsPE/t6O2mT76MkTJ1Jcnz4ioFh8XD+xkX/mjBnEfb97966q84V+gYAgIF24vLDDq8h8i8xuT61IfEX/4P2/i+fpH3/4ocMm2fSSF8uWLVlCH/79A/r4w48ofdUq+utzY6hPj5606bvvOqwDB4CALwlIFS6/s+Vnx/CQUGJDC/5uRSopKRELUq+MG0ccvsSdxFfllldm7is/l0+ZNFn4v/rjjz/cqQbHgIBPCEgTLv/w2aNFSGAQvTJuvKUeLXZu3y7+szh/7pzXEDMzdom6vj9x0uu6UAEImEVAmnDZL/LTo0ZTz+gYKjhzxqz+tquXb5M5ZMmEN96gu42N7cqNZuzbu5e6hkfQ8WPHjJ6K40HAMgLShPvW2jeFoQUbQFiZ8vfvF0KTYeDB/wmwYUZoUDBxDCMkEFCVgBThFpwpEFHjZ6XOtHRFlld/eRFs9IiRVHb9ukvGfAufNncuDR00iJri7FZVVYnVY7Z5bmhooMaGBmGwcfz4cfF8y+NAAgGVCXgt3LKyMuIQHmxsYZWhRRPQvXv2EIcs0bNLrq2tpf59Y4V544H8fHFq6ZVSGjJoMPFroJdffIneePU1emroMOrZPZr4lRDbVyOBgMoEvBIuG1qsTU8X4uFVZHdXdGUBuXjhAuXn5dHvlZWaVfLK8Z6sLPris8+psqJCHMdX6oJfz1BWZiZ9+cUX9Nknn9DWzZvph3/9i27fvq1ZFwpAQBUCXgn32JGj4kr2wpjnW71aUWVw6AcIOJWAx8JlB+Zs65vQrz9VlD+6kjkVEsYFAqoR8Ei4vODDhhYcmnLDuvWqjQn9AQHHE/BIuPtz88Rz7fix4yw1tHD8bGCAIOAmAcPCvVJyhUaNGEndIiLhF9lNyDgMBGQTMCRcXjXmDegchZ1dv/AtMxIIgID1BAwJ9/Sp0xTYKYDmzp5jfU/RIgiAQDMBt4VbfqNcWCk9mZQszelbcy/wAQRAwBABt4TbUN9AK5evoOCAzrTum28tN7QwNCIcDAJ+QMAt4bLHxOiobvTCmDGW2iL7AX8MEQQ8ItChcNkg/8Xn/yoCUHMwaiQQAAHfE9AVLq8ar01fIwwtvlsPQwvfTxd6AAKPCOgK99CBg2K73uuvvkYctAsJBEBADQKawmWPFsMGDxEeLU798osavUUvQAAEBAGXwuWN5RwRgA0tNn23EYYW+LGAgGIEXAr3px9/Es+1M2ek4tWPYhOG7oAAE2gn3Krbt4VzcPZoUXi+EJRAAAQUJNBOuOmrVotb5G+++pru3bunYJfRJRAAgXbC7dE9ml5+4UWCQ3D8OEBAXQLthNszpgfB0ELdCUPPQIAJtBPu5o2bQAYEQEBxAu2EW3W7SvEuo3sgAALthAskIAAC6hOAcNWfI/QQBNoRgHDbIUEGCKhPAMJVf47QQxBoRwDCbYcEGSCgPoH/D2yxPMTI8gT1AAAAAElFTkSuQmCC[/img][br] [br]Find the value of [math]\frac{d}{c}[/math].
The diagram shows two nested triangles that share a vertex. Find a center and a scale factor for a dilation that would move the larger triangle to the smaller triangle.
Where is the center?
What is the scale factor?