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Topic: 5.6 Hinge Theorem Objective: I will be able to use inequalities to make comparisons in two triangles. ���� JFIF H H ��3Exif MM * � � � ( 1 �2 �i , com.apple.print.ticket.itemArray 1 . com.apple.printingmanager 5 #32. com.apple.print.ticket.privateLock 2007-02-13T23:54:45Z com.apple.print.ticket.stateFlag THEOREM 5.13: HINGE THEOREM If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is _____ than the third side of the second. 3 !1AQa"q�2���B#\$R�b34r��C%�S���cs5���&D�TdE£t6�U�e���u��F'���������������Vfv��������7GWgw�������� 5 !1AQaq"2����B#�R��3\$b�r��CScs4�%���&5��D�T�dEU6te����u��F���������������Vfv��������'7GWgw������� ? stream 1 com.apple.print.pm.PostScript << /ProcSet [ /PDF /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R >> com.apple.print.PageFormat.PMAdjustedPageRect endobj com.apple.print.ticket.itemArray 734 digital. com.apple.print.ticket.creator 4 0 obj com.apple.print.ticket.client com.apple.print.pm.PostScript {�,�=��"ʒhm�""�̱�Y.дQbX��ᚴ�u|��~E�ƛ����wb,�"N��LW�����>6�a.n� com.apple.print.ticket.itemArray com.apple.print.ticket.stateFlag com.apple.print.ticket.itemArray The Hinge Theorem is stated, but not proved. In class on Friday, 5/16/2003, I did not cover these very well. 734 Name: Use your knowledge of the Hinge Theorem and its converse to complete each of … com.apple.print.pm.PostScript PQ < SR. 15. • Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. com.apple.print.PaperInfo.PMUnadjustedPageRect Teacher will have a Q & A session over quiz. com.apple.print.ticket.client PDF (633.87 KB) Inequalities in Two Triangles with the Hinge Theorem and the Converse of the Hinge Theorem Foldable for Geometry Interactive Notebooks.This foldable provides a quick overview of the hinge theorem and its converse. xEO� Activity: Warm -Up Quiz T riangle Proofs #2 Students will have 5 minutes to complete the warm -up quiz over Triangle Proofs . IntGeom6.5_Day_1.notebook 1 January 09, 2017 6.5 The Hinge Theorem and Converse 5. A C B D F E EF > BC IFF ∠D> ∠A endstream << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs2 16 0 R >> /Font << /F1.0 17 0 R This PDF can be converted to an interactive version that students can complete from any device on TpT’s new tool. Multiple Choice In the diagram, which of the following is not a possible measure for AB C Hinge Theorem Given that two sides of a ∆ are ≌to two sides of another ∆… The angle between is greater in one triangle IFF the side opposite is greater in that triangle as well. How to use the Hinge Theorem to write an inequality How to use the Hinge Theorem to determine possible angle measurements. com.apple.print.ticket.APIVersion com.apple.print.ticket.modDate Multiple Choice Use the Hinge Theorem and the diagram below to choose the state- ment which must be true. . com.apple.printingmanager 2 0 obj Included angle is the angle formed by the congruent sides. com.apple.printingmanager 21 17. com.apple.print.pm.PostScript View hinge_theorem answers.pdf from ALGEBRA 2 MTH204A at iCademy Global. 2007-02-13T23:54:45Z �� x �" �� com.apple.printingmanager By the Hinge Theorem. ��? com.apple.print.PageFormat.PMVerticalRes stream 576 18. 00.20 View Hinge_Theorem_WS.pdf from MATH MISC at Hewitt-trussville High Sch. 251 1 Students will exchange and grade papers. com.apple.printingmanager com.apple.print.ticket.stateFlag com.apple.printingmanager true /ColorSpace 20 0 R /Intent /Perceptual /BitsPerComponent 8 /Filter /DCTDecode 1 /BBox [106 308 687 392] /Resources 14 0 R /Group << /S /Transparency /CS Within the foldable students … com.apple.print.PageFormat.PMAdjustedPageRect NAME UNIT # ASSIGN # TRIANGLE INEQUALITY THEOREM If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side THEOREM com.apple.print.PageFormat.PMVerticalScaling -18 endstream com.apple.print.ticket.client Problem 3 Point out that students have made a conjecture. This worksheet reviews the Hinge Theorem and its Converse and provides plenty of practice problems! com.apple.print.ticket.itemArray com.apple.print.ticket.modDate He has one �P�?������@�p����>�T�S�z����������*�Jz�Q��>��~����RIOU���>�������RIOU�7������x\�I)��F����m�����ʤ����o��%���>�T�S�og��%���>�T�S�z������F�����RIOU���>���p{��\$������)�Photoshop 3.0 8BIM% 8BIM� � This suggests the Hinge Theorem. Definition of Angle Bisector – says that “If a segment, ray, line or plane is an angle bisector, then it divides an angle into TWO equal parts.” #33. 37m, 35m, 18m 3 ft, 3 ft,6ft Jeremy wants to build a triangular toy using sticks. Consider the two triangles below. Theorem 5-15 Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. com.apple.print.ticket.client com.apple.print.ticket.APIVersion ������E��>�"�"�5����hDkRR�i�DkJM� )Mj�j�Z�֤�!��|QT��\$�;#� Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. com.apple.print.ticket.stateFlag << /Length 9 0 R /Type /XObject /Subtype /Image /Width 1024 /Height 768 /Interpolate << /Length 5 0 R /Filter /FlateDecode >> You may have explored this idea when you studied congruent triangles. 72 *�\$��\$���R%D���*&\$�2��(o�� 576 Hinge Theorem C. Converse Hinge Theorem 17 D. Third Angle Theorem E. Answer not shown A. less than 7 feet B. between 7 and 10 feet C. between 10 and 17 feet 21 D. greater than 17 feet E. answer not shown 18 22 A. x < 9 B. x > 9 C. x < 3 com.apple.print.ticket.stateFlag com.apple.print.ticket.modDate The Hinge Theorems Class _____ ©2011 Texas Instruments Incorporated Page 1 The Hinge Theorems Problem 1 – SAS Inequality Theorem The SAS Inequality Theorem states: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of … . com.apple.print.PageFormatTicket 72 12.) com.apple.print.PaperInfo.PMUnadjustedPageRect com.apple.print.PageFormat.PMAdjustedPaperRect 1) ml-I, mL2 12 10 c 7 4) HJ,KP 850 D 2) my-I, mZ2 5) mZl, mL2 2 8) FH,GE 12 100 8 30 12 3) XB,ZB 240 260 6) mL3,mZ4 16 16 700 870 Choose from 33 different sets of 5.14 Hinge Theorem flashcards on Quizlet. com.apple.print.ticket.stateFlag 0 8 0 obj endobj Longest Side Vs. com.apple.print.PaperInfo.PMPaperName In triangles that have two pairs of congruent sides , there is a r elationship between the included angles and the third pair of s ides. They will prove the converse of the Hinge Theorem in Lesson 48. endstream WX > ST Converse of the Hinge Theorem com.apple.print.ticket.modDate 6 0 obj com.apple.printingmanager 00.20 �GpCpIH���`��GpB�{O��������#�[L�#�Z��6[M(�II��&��%%j#BQ�� ��T�JQ Students will write a two-column proof for this theorem in Lesson 42. > C. = 16 D. cannot be determined E. answer not shown 20 What is the reason for your answer in question 19? distance CB increase. &&66\$5*80(176:ULWHDWZR -column proof. com.apple.print.PageFormat.PMAdjustedPaperRect Given: , K is the midpoint of m SKL > m QKJ Prove: RS > QR 62/87,21 … endobj com.apple.print.pm.PostScript com.apple.printingmanager A�9H9%&O�9>����L\��%!%3. Given sides of 7 cm and 4.2 cm with a non-included angle of 30 , there are two triangles that can be created. >> com.apple.print.ticket.stateFlag com.apple.print.PageFormat.PMScaling Use the Hinge Theorem to complete the statement below m/ . -18 xe��j�0��~�yyW�Zro��@��z.ƅ���?���+�N�6�`wgf?uxEfe6D���f�2�����xC��� �PݍXK�;��w�����E�*��u_�_��A����pĆ�u�(�T'�O'���}B�t�-���OS#-�n_�/�v�������&�U���. 594 •Converse of the Hinge Theorem Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. �I��d�LdT��e����+C�}��'�uY�ӆ|�!D�Fg) �=-��'c �Ǖ���=Z%錭GII-,X�|X��V���\$�{E�t9Rpvv"9��ߍT6N�cFLfڽc���q�!b�c��!dv������C']м�h�>���]��t�v���G�����}�Iy�9#>{�[*伫�=�3�O�7��R�����|̒s�0,0�+I[,d���z���dM\Y�ۍ\$Z�۰ com.apple.print.PaperInfoTicket The Hinge Theorem: If two pairs of sides between two different triangles are congruent but the third pair of sides is not congruent, then the triangle with the _____ included angle will be opposite the _____side. endobj 0 com.apple.print.PageFormat.PMOrientation 14 0 obj com.apple.print.PageFormat.PMVerticalScaling 0 Geometry 33 Standardized Test Practice Workbook 1. SOLUTION: In this figure, we have two pairs of congruent sides and the side opposite from the 41-degree angle is greater than the side opposite the (2x – 7) degree angle. >> 12 0 obj QB) 12 10 ml-3 = ml-2 m 1.2 m 1.2 m 1.2 rnL I rnL I rnL I rnL I . >> com.apple.print.ticket.itemArray 11. Angle Bisector Theorem – says that “If a segment, ray, line or plane is an angle bisector, then it divides an angle so that each part of the angle is equal to ONE HALF of the whole angle.” By the Hinge Theorem, XW < XY. 3<+2 . 8BIM� x H H �@����Rg(� H H �( d � h � 8BIM� H H 8BIM&. 13 0 obj com.apple.printingmanager com.apple.printingmanager com.apple.print.ticket.itemArray the included angles are not congruent, the longer third side is opposite the larger included angle. endobj 0 The Hinge Theorem is a geometric theorem that focuses on this idea. Hinge Theorem and its converse. 6. Learn 5.14 Hinge Theorem with free interactive flashcards. com.apple.print.ticket.client -18 2007-02-13T23:54:45Z Tell whether the side lengths can form a triangle. Hinge Theorem The student is able to (I can): • Analyze the relationship between angles and the sides opposite them • Use the Hinge Theorem to solve problems 2. HINGE THEOREM OR ITS CONVERSE 11.) na-letter 2007-02-13T23:54:45Z com.apple.print.PageFormat.PMOrientation com.apple.print.PaperInfo.PMPaperName 0 Geometry Cheat Sheet Chapter 1 Postulate 1-6 Segment Addition Postulate - If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. A. Triangle Inequality Theorem B. 774 %��������� 0 0.0 endobj Multiple Choice Use the diagram to deter- mine which of the following is a possible length for A 10 B 12 C 13 D 15 E 17 2. . com.apple.print.PaperInfo.ppd.PMPaperName com.apple.print.ticket.modDate com.apple.print.ticket.stateFlag com.apple.printingmanager BC = 9 inches: XZ= 11 inches: and Hinge Theorem to determine that, since 17 in. 2007-02-13T23:54:45Z > 12 in., the angle of the opening of Shawn ¶s locker is greater than the angle of the opening of Neva ¶s. to the Converse of the Hinge Theorem, m D > m A. endobj 0 com.apple.print.ticket.privateLock com.apple.print.ticket.stateFlag com.apple.print.ticket.type Find the range of possible values for x. If two lines in a plane are parallel, then the two lines do not contain two sides x�Ё � ����Pa��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`��0`���2Z& Begin the discussion by reviewing the triangle inequalities covered in Lesson 39. com.apple.print.ticket.client 5-6 Hinge Theorem-- Ch. com.apple.print.ticket.client 2007-02-13T23:54:45Z WX > _____ THEOREM 5.14: CONVERSE OF THE HINGE THEOREM endobj Longest Angle Smallest Side Vs. Shortest Side Angle-Side Relationships in Triangles (5.9) com.apple.print.ticket.creator com.apple.print.ticket.creator �����2�)PYW��jŲ݊"���6�(�ωt`GC���J� B�zq~����k���M� �6�]8I�\$���X,�XI��T�����࿢,�T&N�'�X����!˓�N�����}�EVE�u��� �']٥��(NI�Ϻ�7�tu��IW��TtŚ����U�+7���jlI��B4_j��+�h�v�� ��*Pa�`��R'��R��9��؃yÜ~8���at%���JBU00��U�w��PVD���]��e��P� E`e�-�a_=tZ�j�b�3�T��ӏ�)�r�y�́�E�o?k�}�W��]�"ܜ�`꟭����Y��Y��,H�O�P��aH�xrk�������h���ҙ�V&. 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Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: com.apple.print.ticket.modDate com.apple.print.PaperInfo.PMUnadjustedPaperRect com.apple.printingmanager ���p�`�!�a&���1#8R����'p�q�IBT,7LhOk���)x��v5��J;�7�W�j\�����:�y�1}%,�kRF�����H]Pk �#�h/BA�cw�GAz��R�=��T{�c�0� 5. How to use the hinge theorem to find possible values for x. . and . com.apple.print.PaperInfo.ppd.PMPaperName >> >> com.apple.print.ticket.itemArray Students will be able to apply the Hinge Theorem or its converse to make comparisons in two triangles. . 5 0 obj US Letter 2.5.4 Hinge Theorem 1. 159 %�%5�J��|Շ5 � )��'4�N�%5� 36 (X+ 18)' 1260 ax-8 Write a temporary assumption you could make to prove the conclusion indirectly. Use the hinge theorem or its converse and properties of triangles to write and solve an inequality to In AABC and A-XYZ: AB = AC = m L A = 470 Which of the following is a possi draw a picture!) A�� II� 4. << /Length 13 0 R /Filter /FlateDecode /Type /XObject /Subtype /Form /FormType com.apple.print.ticket.creator 3. 16 0 R /I true /K false >> >> m/ , so LN. stream 2003-07-01T17:49:36Z %PDF-1.3 com.apple.print.ticket.stateFlag com.apple.print.ticket.modDate com.apple.print.ticket.client com.apple.print.ticket.creator Theorems 5-13 and 5-14 The Hinge Theorem and its Converse two sides of one triangle are congruent to two sides of another triangle If . com.apple.print.PaperInfo.PMUnadjustedPaperRect com.apple.print.ticket.creator < B. 15 19 A. a) Use the Exterior Angle Inequality Theorem to list all angles whose measures are less than m 14. b) Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than m 5. com.apple.print.PageFormat.PMHorizontalRes The hinge theorem is a useful theorem in real-life applications. �C�?�S���Y�G�)>��Ȧ�� �tO�Jd� P\$IIA)䡂����qO� com.apple.print.ticket.modDate The Converse of the Hinge Theorem: If two pairs of sides between two different triangles are … 300 - 3X+2 7 . 13.) com.apple.printingmanager Postulate 1-7 Angle Addition Postulate - If point B is in the interior of AOC, then m AOB + m BOC = m AOC. com.apple.printingmanager -18 com.apple.print.ticket.modDate com.apple.print.PageFormat.PMScaling �@��+�Ӥ���UQ���e� Worksheet 5.6 Hinge Theorem Chapter 5 Name Refer to each figure given write an inequality relating the given pair of angle or segment measures. 5 6 Inequalities in Two Triangles and Indirect Proof In Exercises 1 and 2. list the sides or angles in order from least to greatest. 10 0 obj com.apple.print.ticket.client 0 0.0 com.apple.print.ticket.itemArray �� 'Adobe Photoshop CS2 Macintosh 2007:02:13 15:54:45 � �� � � z �( � � H H ���� JFIF H H �� Adobe_CM �� Adobe d� �� � . << /Length 11 0 R /Type /XObject /Subtype /Image /Width 583 /Height 86 /Interpolate com.apple.print.ticket.client 2007-02-13T23:54:45Z Name _ Date _ Class_ LESSON 5-6 Reteach Inequalities in Two Triangles Theorem Example Hinge Theorem If two sides of one << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 792 612] 2003-07-01T17:49:36Z com.apple.print.ticket.type 11 0 obj Multiple Choice Use the diagram and the Hinge Theorem to choose the inequality that correctly describes the restriction on the value of x. 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