IM Geo.1.21 Lesson: One Hundred and Eighty
Here are 2 lines l and m that are not parallel that have been cut by a transversal.
[size=150]Tyler thinks angle [math]EBF[/math] is congruent to angle [math]BCD[/math] because they are corresponding angles and a translation along the directed line segment from [math]B[/math] to [math]C[/math] would take one angle onto the other. 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7Y3/w2omNVkBErU+y2bdu6lWDsiJG2q9GjRzsGffv2zURRL/1MgGwokfcuz1kMi+zbVNZfgpUC2kxTWVxgxQzbG464rI6x4sk0E3sOdjdiI7G5EexbunRpZ3tjxEbgLzeJJ2433nijDRo0yMaOHWvPP/+8vf766872xugGexFTYQTOcw1JQROzvQR16NOnj4vvRJBVgkWAH2DuTfqRH07cjwoyrlOC5aP7B2HjpmBkhaMs4oYgjRs3zoYOHeoErkePHm56is/SKaecYqyUYmPDDw5xQ/BYWCAdS+vWrd1KHQLHwgKGcRYpEDimZ8T5cT2um8jiOQ0z7cNOiJsDMYYqwSPAj2UyR8Xk4o/HlinBCt49ZPv27XO/cogNU1JWNel0YigRIwLDCT4mK+cVV1zh7EkIGHF93giOaSmLCtjkEDt834huYHqKzY7MnriF4NTJYse6deuM/GM5FWx/bA+PYLIKe+qppzq3E4XZ5ETN35+RLSO3xa68tgBXJtyOWPmPTBGV0/kkWDnRCcFnrJwynMf+hTc6ox7PE50bkRtmzJgxdueddzpxO++889zUlFXTzLYLXnMDlylTxo3usFf16tXLiSMjKM/Q7n2PbBpMIVSCSYAIFPoS+yP3CFN6Rv2JcvdhlsCPL8LFPRlLkWDFQinNj0HwmKYSAE8GBexnRC1ge8MlhJGaJ1KZH0mmyNS1VatWzl6HMd4LyWJkiD2EKSnX4ObVJrj+udkQqSOPPNKNvLFjMWLGsTsRhbA+zBwUTBWxFglWrKR0XI4E+NVlShkpWNjWiBnF3YGQLOJCGXXhyItDcKFChdzx3qop4sc/BvGmLEYQ7YCLBA7CTCux67F6unr1arewQAZSQrIQOpXEEyCQvUuXLok/sZm7F7Bf4ZdHwoRYiwQrVlI6LlsCBDpju8IW1qxZMxcPyiOG/YMVXDOwv+HQy/6CeLsTnoPdjFUp/lGIWMCfDduaF61A6iOcTrGRYY/DL46RG9lFsLuxXT1xq6zC4vtGSBYOwwgcvmJMi1ViJ0AmFlx1El24L8h5ht2KRaB4igQrHlo6NgsBfiVZqUREEAimeIhEIvKvM3LaunWr80Vj+kjaazKFeCunLCzgGtK9e3e3GsnojOknIzXEk9Eciwr4vBFsT+YIBA4/OVZOGf3h2IvvG9Nd3EJYXCgoH6MscAvwDexXhMLh8Jzowo8KC0I4Zsdqu6IOmA0kWInujTQ6HxlfCWHCc70gjes40mIHw/fMWzll9MY/GyM4VjrHjx/vRmAEx7MSyiomIwhGbNjZDj30UDc9JcvEscce60KHEDl837yohVGjRtnUqVPtgw8+cClzIuMmw9bts2bNcmFr8QhKrAxY4GnRooUb+cb6HY7LksAvni/r2PQmgN0Be1WybBzJpotxnxEcrhrk4MIWxhSFqAVWPIcPH27EQhKSxcitcuXKTpwjbXSRz4lq4DgyhjDqYxTx2muvudEm09GgFcQhWVlNEKx4p4IeP42wPBJ6jIkANzL/kPyzstKTroXgeqa+r7zyilsY4J/Qy9RLYLe3oBApajxnRRUHX8TNyxbCahkiycIC25oxquH8uKEgpIgqixp+C8nKS99jQqDd77zzjvs607zc/PsiryPBiqSh5zkSYATCiKNEiRLOqTTHg/WhI4DfG9NTppHY3h555BEXFI/RGXsaIVfY/1hQwGbEFnW4EmB74302BcZfiTTkxGviUoJrAQsV+EQx5SXkC7cTQrKw+TE9jkXccDomvIv8c8lyDo28DRBdxIl6E3tLfRmFxpMSW4IVSVTPsyXATYVBm9EBxnWVxBFgesoiBUv82N0YfWArY1pJKiRSKyFwhDkhXl7EAqun9AcLDCx8eAsLOPR269bNrZwicPhTsXJKFARTXvqSP2JXvREgIsmCQyoKwoWAE1hNm+MpEqx4aKXpsazOEZCNcR0XBpWCIcCoiSkiCwv8ozO9wkWAlVNsiiwsMFpiBQ6Bw58N1w9cQxA07GxsHMNIjhGdJ1beI+FbeLPjYsJUl3MTTM+ozS9FguWXnvBpPQjd4YZmZU1e6D7tpINUi1EMU0PsYBj9mc7jj8b0FKHD580TKu8RIWMayqP3Ho9FihRxjr44/DIqI6iejWQYvRFvimByzlQsLkiwDtLZeut/BAij4Ybt16+fkISMAIIWGZmAOwcG8MiC4GEbY+r2r3/9ywYOHGhklmXKiUsI7iCRwhb5nPRITFGJL2VnLbKFEJKFuwQ+dXn1dZNgRfaQnjsCrFBdeOGFLtB50qRJohJiAoQ9MUqKxUifEwZGcqQrwr5JvOngwYNdYDz3EQsLBNMTjsVoLVLYsJ1hiyNsC3HD9sYPJD5vOPNmLhKszETS/DUpYliZwt6RXWhNmiNS8/NBAGFjako6JBx6EUumpyws4NOHaBGRwEIC8aeZiwQrM5E0fk1wMQ6S3DAseauIQEERIMTrYDYxCVZB9YjPrssqE86ODOFZiVIRAT8SkGD5sVdSXCd8fbArkPEAT3YVEfArAQmWX3smBfXC65gRFWKF57GKCPidgATL7z2UpPqRaYAMkmQmiGcTgCRVR6cVgZgISLBiwhSug5YtW+ZyRSFYX331Vbgap9aEmoAEK9Tdm7VxJE3DH4Z8ROSPUhGBIBGQYAWpt/JZV89zHZ8XpQvOJ0x9vUAISLAKBHvqL0qedIzrOOqpiEBQCUiwgtpzcdSb3XuLFy8u43oczHSoPwlIsPzZLwmpFRH0bMRAziSCWFVEIOgEJFhB78Fs6s929eQ+IiI/ETvYZHMZvS0CKSUgwUop7tRcjP35SGOMcV1hNqlhrqukhoAEKzWcU3YV9uhjyypydauIQNgISLBC1KMNGjRwK4EHyyMUomaqKWlMQIIVgs5fsmSJ2/iTLaRStZFACLCpCQEkIMEKYKdFVpmto8qUKWONGzeW53okGD0PJQEJVoC7ld2JEas+ffrEtRllgJusqqc5AQlWQG8ANtXEGXTkyJEBbYGqLQLxE5Bgxc+swL9B3mvCbNiCS0UE0omABCtAvc1uveSvYmTFZpoqIpBuBCRYAelxduIlLQye6+wXpyIC6UhAghWAXh8zZozbKr5Hjx4BqK2qKALJIyDBSh7bhJz5tttus2LFihnhNtoqPiFIdZIAE5Bg+bTz9u7d67YEx7iOr5WKCIiAmQTLh3fBN998YxUrVnRbxbMTs4oIiMD/CEiwfHYnzJo1ywixqV+/vs9qpuqIQMETkGAVfB9k1GDixIluJfCKK66QvSqDip6IwB8EJFh/sCjQZ3379rUiRYrYP/7xD9u3b1+B1kUXFwG/EpBgFXDP/Pzzz864XrhwYXvuuecKuDa6vAj4m4AEqwD7B+P6ySef7EZWq1evLsCa6NIiEAwCEqwC6qfPPvvMZVqoW7eu/fbbbwVUC11WBIJFQIJVAP3F7suHHXaYde7c2fbv318ANdAlRSCYBCRYKew3PNXvvPNOl2kBD3aNrFIIX5cKBQEJVoq6ka22GFEVKlTIJk+enKKr6jIiEC4CEqwU9CfGdTaIIDsoKWJUREAE8kZAgpU3bjF/i9W/ChUqWM2aNW39+vUxf08HioAIZCUgwcrKJGHvELRM8HK7du3kDJowqjpROhOQYCWh9w8cOGD33XefEyuM7CoiIAKJISDBSgzHjLP89NNPduWVVzqxmjJlSsb7eiICIpB/AhKs/DPMOMPGjRutSZMmzmb1/vvvZ7yvJyIgAokhIMFKDEdbtmyZVatWzerUqWNLly5N0Fl1GhEQgUgCEqxIGnl8/uqrr7opYPPmze2HH37I41n0NREQgdwISLByI5TL50OHDnVidc899+RypD4WARHILwEJVh4J7tq1y3r27OnESp7reYSor6UlAS8kbdu2bRaZpYS42rVr19qWLVuy5SLByhZN9h/gud66dWtnXH/99dezP1CfiIAIRBFgjwIy606dOtXYtq5hw4ZuR6gdO3a45JUXXnih23szu70M0kqw1q1bZ9ddd52dffbZDkrXrl3tq6++igKa24sFCxbYiSee6Izr8+fPz+1wfZ5EAnPnzrUWLVpY48aN3c0/duxYbTKbRN6JOPV7771nRx99tF1wwQWG7XfmzJlulkLG3ccff9wWLVrk/r+uvfbag14ubQRrzpw5Vrp0aUPBSe8ybtw46969uzFairVMnz7dwW3ZsmVc34v1/DouPgL9+/e3448/3h566CEj+0W5cuXcL7YWPuLjmMqjn376afc/NHv27IzLEg1y6623Zry++OKLLa0Fa/PmzQ4SCp7X8sQTT7hz3H777Xk9hb6XQALbt293Pm+DBw/OOCt2xWOOOcY57ma8qSe+IUB6pWuuuca6deuWUSdsVggWj14hXTij5YOVtBhh4RvVpk2bg7U/1/eAfOONNzqozz77bK7H64DUEFizZo3Vq1fPGPVGFkbOTNkVaB5JxR/P2b/g3HPPdSNir0bDhg2z6tWrey/tu+++c/9r2RneQy9YNBwFX7VqVQaUWJ9g8zr//PNdWhiMhCr+IeDZEhcuXBhVqTfffNNtQpuX/o46kV4knACRIDhXY57xSseOHd2AwHs9bdo09//qvc78GHrBwuUAwYq3fPTRR3bSSSdZrVq17IMPPoj36zo+yQSwQ9I3JEaMLOPHj7fTTjvNMAOo+IvAO++846bsGzZsyKjYoYceGpXQ8pZbbnEj54wDMj2J/z850wn8/nLChAluV5p46vnKK69Y8eLF3eiKUZaK/whgC+HXOXO56qqrrEOHDpnf1msfEGBXc1YDvfLrr79a06ZNLfJ/7P777zfsxdmV0AuWtyqRHYDM77M3ICOy66+/PvNHeu0TAnv37nWuDA888EBUjZj+s7nHM888E/W+XviDAA6j9J1XsA/v3r3be+ke9+zZk+PGLKEXrO+//94JUKQ3OvmqDra78k033eSOfeqpp6Ig6oW/COzcudMqVapk/GJT8JDeunWr67tOnTr5q7KqTUIJhF6woNWvXz9jrozf1aBBg5yPx8iRIzNA4lXbtm1bYzlVxvUMLL59grMvo+DevXu7RInt27e3kiVLRk03fFt5VSxfBNJCsCD00ksvOW/oSy65xG644QbDS5oyb94857WOgf3jjz/OF0x9OTUEWBkkSqFLly5OpB555BHLvFqYmproKqkmkDaCdTCwhAWwkw2uC99+++3BDtF7IiACPiKQtoI1adIkN60gAPNg9iwf9ZGqIgIi8P8E0kawsFlh5yhfvrzVr1/fiRUxaCr+JDBq1CjXR8R/Kje+P/uoIGoVJVistBDSwPQoLH8EwhJoiZE28u/hhx82/EDwvg1LW8PQDhxBR48eHdVX+MQxIsZtIQxtVBty1xeSEmzatCmLJkYJVp8+feyII45w3qgEkYbh77jjjnNtihQrntNORlthaGOY2sCms5n7itdFihQx+jJMbVVbsteYUqVKudRBmRUrSrDYSIGEdMRjheHvrbfecvl1WE3K/E/Ar/jbb78dinaGoa+8Nrz77rtG2pjI/mKENWTIEBeD5h2nx3D8j2bXjzNmzDDC4zKXKMHK/GEYXpMkrESJEtaqVSurUaOGValSxSJ9sMLQxrC1AQ/oe++91zmHknkBtwUVEYBAqAXrrrvucr/U7MLMPwEBsQebF+tW8B8B+osoBfqMyAQVEYBAKAWL5G5kBWVa8fLLL6unRUAEQkIgdIL19ddfO8/1ypUr2/Lly0PSTWqGCIgABEIlWOy4XLZsWbfJhDJO6gYXgfARCI1g4adDgDMxZviTqYiACISPQOAFC4MsG0NgryIrg4oIiEB4CQResNgSCLGKzHcV3u5Sy0QgvQkEVrBYCcSvir3oVq5cmd69qNaLQJoQCKRgkcDtqKOOslNPPTUqH3Sa9JmaKQJpSyBwgjVx4kS3QQQZQrdt25a2HaeGi0A6EgiMYJG3G8/1okWLOiM7ntAqIiAC6UUgMIJ1+eWXW7FixYz96FREQATSk0AgBAtb1ZFHHmnvv/9+evaSWi0CIknp9u4AAAOgSURBVOAI+FqwVqxY4UZVVatWdYnb1GciIALpTcC3gsWGptirWrdubbt27UrvXlLrRUAEHAHfCRbG9IEDB7ocVniwq4iACIiAR8B3gnX11Ve7rbeeeOIJr456FAEREAFHwFeC1aBBA2ezIj2qigiIgAhkJuALwVq1apXbFIJNBtauXZu5jnotAiIgAo5AgQvW1KlTXfBy8+bN1SUiIAIikCOBAhWs4cOHu5jA3r1751hJfSgCIiACECgQwSLMplevXs64rh1sdCOKgAjESiDlgsVuy2eddZbzXH/xxRdjraeOEwEREIHUjrDYFp60MORd/+KLL4RfBERABOIikLIRFhuakhmU0ZWKCIiACOSFQEoE69FHH3VuCz169MhLHfUdERABEXAEkipYu3fvNlYAybQwePBgIRcBERCBfBFImmDt2LHD7Q9YpkwZI5BZRQREQATySyApgrV69WqrVKmS+9Puy/ntIn1fBETAI5Bwwfrwww9dPGCtWrW8a+hRBERABBJCIKGCNX78eLcSeNVVVyWkcjqJCIiACEQSSIhg7dy50/r06WNFihSx++67L/L8ei4CIiACCSOQb8HaunWrnXfeeVaqVCmbNGlSwiqmE4mACIhAZgL5Eiw2NK1du7ZVrlzZvvzyy8zn1msREAERSCiBPAvWokWLrHTp0lanTh3lXE9ol+hkIiAC2RHIk2Cx+zJhNpdddll259X7IiACIpBwAnEJ1r59+5xxHbEaMGBAwiujE4qACIhATgRiFqyffvrJOnbsaIUKFbIXXnghp3PqMxEQARFICoGYBAvP9fr16zvj+uLFi5NSEZ1UBERABHIjkKtgzZ8/34XYnH766bZ+/frczqfPRUAERCBpBHIUrGnTpjnjetu2bY0poYoIiIAIFCSBbAXr5ptvdmL14IMPFmT9dG0REAERyCCQRbB27dplXbp0cWKlnOsZnPREBETABwSiBGvNmjXWqFEjK1++vH366ac+qJ6qIAIiIAJ/EIgSrK5duxppYZTD6g9AeiYCIuAfAlGC9cYbbxjbxquIgAiIgB8JRAmWHyuoOomACIiAR0CC5ZHQowiIgO8JSLB830WqoAiIgEdAguWR0KMIiIDvCUiwfN9FqqAIiIBHQILlkdCjCIiA7wlIsHzfRaqgCIiAR0CC5ZHQowiIgO8JSLB830WqoAiIgEdAguWR0KMIiIDvCUiwfN9FqqAIiIBHQILlkdCjCIiA7wn8H/amLer74YsIAAAAAElFTkSuQmCC[/img][br]Here are his reasons.[br][br][list][/list][list][*]The translation takes [math]B[/math] onto [math]C[/math], so the image of [math]B[/math] is [math]C[/math].[/*][*]The translation takes [math]E[/math] somewhere on ray [math]CB[/math] because it would need to be translated by a distance greater than [math]BC[/math] to land on the other side of [math]C[/math].[/*][*]The image of [math]F[/math] has to land somewhere on line [math]m[/math] because translations take lines to parallel lines and line [math]m[/math] is the only line parallel to [math]l[/math] that goes through [math]B'[/math].[/*][*]The image of [math]F[/math], call it [math]F'[/math], has to land on the right side of line [math]BC[/math] or else line [math]FF'[/math] wouldn’t be parallel to the directed line segment from [math]B[/math] to [math]C[/math].[/*][/list]Your teacher will assign you one of Tyler’s statements to think about. Is the statement true? Explain your reasoning.[br][br]
In what circumstances are corresponding angles congruent? Be prepared to share your reasoning.[br]
Use the applet below to create a triangle
[list][*]Use the Text tool to label the 3 interior angles as [math]a,b,[/math] and [math]c[/math].[/*][*]Mark the midpoints of 2 of the sides.[/*][*]Extend the side of the triangle without the midpoint in both directions to make a line.[/*][*]Use what you know about rotations to create a line parallel to the line you made that goes through the opposite vertex.[/*][/list][br]What is the value of [math]a+b+c[/math]? Explain your reasoning.[br]
Use the same applet above.
[list][*]Translate triangle [math]ABC[/math] along the directed line segment from [math]B[/math] to [math]C[/math] to make triangle [math]A'B'C'[/math]. Label the measures of the angles in triangle [math]A'B'C'[/math].[/*][*]Translate triangle [math]A'B'C'[/math] along the directed line segment from [math]A'[/math] to [math]C'[/math] to make triangle [math]A''B''C''[/math]. Label the measures of the angles in triangle [math]A''B''C''[/math].[/*][*]Label the measures of the angles that meet at point [math]C[/math]. Explain your reasoning.[/*][/list]
What is the value of [math]a+b+c[/math]? Explain your reasoning.[br]
One reason mathematicians like to have rigorous proofs even when conjectures seem to be true is that it can help reveal what assertions were used.
This can open up new areas to explore if we change those assumptions. For example, both of our proofs that the measures of the angles of a triangle sum to 180 degree were based on rigid transformations that take lines to parallel lines. If our assumptions about parallel lines changed, so would the consequences about triangle angle sums. Any study of geometry where these assumptions change is called non-Euclidean geometry. In some non-Euclidean geometries, lines in the same direction may intersect while in others they do not. In spherical geometry, which studies curved surfaces like the surface of Earth, lines in the same direction always intersect. This has amazing consequences for triangles. Imagine a triangle connecting the north pole, a point on the equator, and a second point on the equator one quarter of the way around Earth from the first. [br][br]What is the sum of the angles in this triangle?
lM Geo.1.21 Practice: One Hundred and Eighty
The triangles here are each obtained by applying rigid motions to triangle 1.
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[/img][br]Which triangles are translations of triangle 1? Explain how you know.[br][br]
Which triangles are not translations of triangle 1? Explain how you know.
The quadrilateral is a parallelogram. Find the measure of angles 1, 2, and 3.
In the figure shown, lines f and g are parallel.
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[/img][br]Select the angle that is congruent to angle 1.
Angle BDE is congruent to angle BAC.
Name another pair of congruent angles. Explain how you know.
[size=150]Describe a transformation that could be used to show that corresponding angles are congruent.[/size][br]
[size=150]Describe a transformation that could be used to show that alternate interior angles are congruent.[/size][br]
Lines AD and EC meet at point B.
[img]data:image/png;base64,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[/img][br]Which of these [i]must[/i] be true? Select [b]all[/b] that apply.
Points E, B, and C are collinear.
Explain why points [math]A,B,[/math] and [math]D[/math] are collinear.
Draw the image of figure ACTS after a clockwise rotation around point C using angle CTS and then a translation by the directed line segment CT.
Describe another sequence of transformations that will result in the same image.
Triangle ABC is congruent to triangle A'B'C'.
Describe a sequence of rigid motions that takes [math]A[/math] to [math]A'[/math], [math]B[/math] to [math]B'[/math], and [math]C[/math] to [math]C'[/math].