hinge theorem pdf

the included angles are not congruent, the longer third side is opposite the larger included angle. << /Length 9 0 R /Type /XObject /Subtype /Image /Width 1024 /Height 768 /Interpolate 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. com.apple.print.ticket.itemArray stream A C B D F E EF > BC IFF ∠D> ∠A 0 > 12 in., the angle of the opening of Shawn ¶s locker is greater than the angle of the opening of Neva ¶s. com.apple.print.ticket.stateFlag com.apple.printingmanager com.apple.print.ticket.stateFlag com.apple.print.PageFormat.PMScaling 1 com.apple.print.ticket.stateFlag 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. The Hinge Theorem is stated, but not proved. com.apple.print.ticket.privateLock com.apple.print.ticket.creator •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. com.apple.print.PaperInfo.PMUnadjustedPageRect com.apple.print.PageFormat.PMVerticalRes com.apple.print.ticket.creator �A�)��'$�NBp�BrJD�'"� �)�� D� 5. +��'�RS��G�#5��"�%j#P�QRRf�V��F��Sk�RpT�B)�$��1rJS��rP�RS'"8�8��nCr��JF�+>��G!�蟁IO��#��Ϣ>T�|QP�S%&iEiU�Q )�Ҧ Choose from 33 different sets of 5.14 Hinge Theorem flashcards on Quizlet. WX > _____ THEOREM 5.14: CONVERSE OF THE HINGE THEOREM 3. Teacher will have a Q & A session over quiz. 5 0 obj com.apple.printingmanager Included angle is the angle formed by the congruent sides. com.apple.print.pm.PostScript com.apple.print.ticket.creator 774 View hinge_theorem answers.pdf from ALGEBRA 2 MTH204A at iCademy Global. 576 Begin the discussion by reviewing the triangle inequalities covered in Lesson 39. com.apple.print.ticket.modDate 3 1100 ALGEBRA Use the Hinge Theorem or its converse and properties of ... Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: . stream Students will write a two-column proof for this theorem in Lesson 42. 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 … << /Length 5 0 R /Filter /FlateDecode >> com.apple.print.ticket.itemArray Geometry 33 Standardized Test Practice Workbook 1. 0 594 -18 �GpCpIH��`��GpB�{O��#�[L�#�Z��6[M(�II��&��%%j#BQ�� T�JQ endobj com.apple.print.ticket.client com.apple.print.ticket.modDate Activity: Warm -Up Quiz T riangle Proofs #2 Students will have 5 minutes to complete the warm -up quiz over Triangle Proofs . com.apple.print.ticket.client com.apple.print.PaperInfo.ppd.PMPaperName 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. com.apple.print.ticket.modDate com.apple.print.PageFormat.PMAdjustedPaperRect com.apple.print.PaperInfo.PMUnadjustedPaperRect 1 &&66$5*80(176:ULWHDWZR -column proof. • Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. Definition of Angle Bisector – says that “If a segment, ray, line or plane is an angle bisector, then it divides an angle into TWO equal parts.” #33. -18 You may have explored this idea when you studied congruent triangles. 16 0 R /I true /K false >> >> 37m, 35m, 18m 3 ft, 3 ft,6ft Jeremy wants to build a triangular toy using sticks. and . 5 6 Inequalities in Two Triangles and Indirect Proof In Exercises 1 and 2. list the sides or angles in order from least to greatest. He has one 72 00.20 Geometry Cheat Sheet Chapter 1 Postulate 1-6 Segment Addition Postulate - If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. com.apple.printingmanager endobj Hinge Theorem C. Converse Hinge Theorem 17 D. Third Angle Theorem E. Answer not shown A. less than 7 feet B. between 7 and 10 feet C. between 10 and 17 feet 21 D. greater than 17 feet E. answer not shown 18 22 A. x < 9 B. x > 9 C. x < 3 2007-02-13T23:54:45Z Theorems 5-13 and 5-14 The Hinge Theorem and its Converse two sides of one triangle are congruent to two sides of another triangle If . xe��j�0��~�yyW�Zro��@��z.ƅ��?��+�N�6�`wgf?uxEfe6D��f�2��xC�� PݍXK�;��w��E�*��u_�_��A��pĆ�u�(�T'�O'��}B�t�-��OS#-�n_�/�v��&�U��. com.apple.print.PageFormat.PMHorizontalRes 8BIM� x H H �@��Rg(� H H �( d � h � 8BIM� H H 8BIM&. com.apple.print.ticket.creator com.apple.print.ticket.creator >> Two Proofs from §15.3 (Hinge Theorem) Note: These proofs should help you prepare for Monday’s test. << /ProcSet [ /PDF /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R >> com.apple.print.PageFormat.PMHorizontalRes ��E��>�"�"�5��hDkRR�i�DkJM� )Mj�j�Z�֤�!��|QT��$�;#� 6. How to use the hinge theorem to find possible values for x. �� x �" �� com.apple.print.ticket.type BC = 9 inches: XZ= 11 inches: and com.apple.print.ticket.client distance CB increase. 0.0 159 com.apple.printingmanager This worksheet reviews the Hinge Theorem and its Converse and provides plenty of practice problems! HINGE THEOREM OR ITS CONVERSE 11.) << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 792 612] com.apple.print.ticket.client /XObject << /Im2 10 0 R /Im1 8 0 R /Fm1 12 0 R >> /Properties << /Pl1 15 0 R com.apple.print.ticket.modDate com.apple.print.PageFormat.PMOrientation 15 19 A. |��II7&��%%3.Q.LJ��D��)r��h��*�'�"�� Y��Ȧ��G�~E0��$��%)8>J2�RS)JTe)IL�JRS)M)�4��RSIM)$�JI%))EA� D� 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�� ? �� JFIF H H ��3Exif MM * � � � ( 1 �2 �i , �� ' com.apple.print.ticket.creator com.apple.print.ticket.stateFlag com.apple.print.ticket.stateFlag 13 0 obj 10 0 obj com.apple.print.ticket.client xEO� com.apple.print.ticket.client Within the foldable students … View Hinge_Theorem_WS.pdf from MATH MISC at Hewitt-trussville High Sch. com.apple.print.PageFormat.PMVerticalRes 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. �� 'Adobe Photoshop CS2 Macintosh 2007:02:13 15:54:45 � �� z �( � � H H �� JFIF H H �� Adobe_CM �� Adobe d� �� com.apple.printingmanager 5-6 Hinge Theorem-- Ch. This PDF can be converted to an interactive version that students can complete from any device on TpT’s new tool. 2007-02-13T23:54:45Z 3<+2 . com.apple.print.subTicket.paper_info_ticket endobj Longest Angle Smallest Side Vs. Shortest Side Angle-Side Relationships in Triangles (5.9) com.apple.print.ticket.itemArray 251 com.apple.print.ticket.client com.apple.print.ticket.stateFlag m/ , so LN. The Hinge Theorem is a geometric theorem that focuses on this idea. com.apple.print.ticket.itemArray -18 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. com.apple.print.ticket.stateFlag This lesson will define the hinge theorem and use it to compare triangles. com.apple.print.ticket.client com.apple.print.PaperInfo.PMPaperName 2007-02-13T23:54:45Z com.apple.print.ticket.itemArray %PDF-1.3 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.” Given: , K is the midpoint of m SKL > m QKJ Prove: RS > QR 62/87,21 … They will prove the converse of the Hinge Theorem in Lesson 48. A�� II� 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!) 12.) endobj com.apple.print.pm.PostScript stream 1 Theorem 5.14: Converse of the Hinge Theorem If two sides of a triangle are congruent to two sides of another triangle and the third side of the first is longer inc\uðecl than the third side of the second, then the ... 20170125073728775.pdf Created Date: The Converse of the Hinge Theorem: If two pairs of sides between two different triangles are … �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{��$��)�Photoshop 3.0 8BIM% 8BIM� � By the Hinge Theorem. com.apple.print.PaperInfo.PMUnadjustedPageRect com.apple.print.ticket.modDate com.apple.print.ticket.itemArray 00.20 Hinge Theorem and Converse If two sides of one triangle are congruent to two sides of another triangle … com.apple.printingmanager com.apple.print.ticket.privateLock << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs2 16 0 R >> /Font << /F1.0 17 0 R 594 2.5.4 Hinge Theorem 1. com.apple.printingmanager Hinge Theorem and its converse. endobj com.apple.print.ticket.creator Find the range of possible values for x. 6 0 obj 5. com.apple.print.ticket.itemArray Students will be able to apply the Hinge Theorem or its converse to make comparisons in two triangles. com.apple.print.PaperInfoTicket *�$��$��R%D��*&$�2��(o�� In class on Friday, 5/16/2003, I did not cover these very well. 11. com.apple.print.PageFormat.PMScaling com.apple.print.ticket.modDate How to use the Hinge Theorem to write an inequality How to use the Hinge Theorem to determine possible angle measurements. endstream com.apple.printingmanager 2007-02-13T23:54:45Z com.apple.print.ticket.stateFlag 0.0 0 8 0 obj Use the Hinge Theorem to complete the statement below m/ . 2007-02-13T23:54:45Z 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. com.apple.print.ticket.creator 1 /BBox [106 308 687 392] /Resources 14 0 R /Group << /S /Transparency /CS If two lines in a plane are parallel, then the two lines do not contain two sides endobj com.apple.print.ticket.modDate 576 Postulate 1-7 Angle Addition Postulate - If point B is in the interior of AOC, then m AOB + m BOC = m AOC. 5 Review.gwb - 22/22 - Tue Oct 01 2013 10:13:00. com.apple.print.PageFormat.PMAdjustedPageRect com.apple.print.PageFormatTicket com.apple.print.PaperInfo.ppd.PMPaperName By the Hinge Theorem, XW < XY. com.apple.print.ticket.client The hinge theorem is a useful theorem in real-life applications. 0 digital. endobj 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. Multiple Choice Use the Hinge Theorem and the diagram below to choose the state- ment which must be true. com.apple.print.pm.PostScript true /ColorSpace 16 0 R /SMask 18 0 R /BitsPerComponent 8 /Filter /FlateDecode %�%5�J��|Շ5 � )��'4�N�%5� Name _ Date _ Class_ LESSON 5-6 Reteach Inequalities in Two Triangles Theorem Example Hinge Theorem If two sides of one com.apple.print.ticket.modDate 2007-02-13T23:54:45Z 2 0 obj com.apple.print.ticket.modDate �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 ��2�)PYW��jŲ݊"��6�(�ωt`GC��J� B�zq~��k��M� �6�]8I�$��X,�XI��T��࿢,�T&N�'�X��!˓�N��}�EVE�u�� ']٥��(NI�Ϻ�7�tu��IW��TtŚ��U�+7��jlI��B4_j��+�h�v�� *Pa�`��R'��R��9��؃yÜ~8��at%��JBU00��U�w��PVD��]��e��P� E`e�-�a_=tZ�j�b�3�T��ӏ�)�r�y�́�E�o?k�}�W��]�"ܜ�`꟭��Y��Y��,H�O�P��aH�xrk��h��ҙ�V&. >> >> << /Length 11 0 R /Type /XObject /Subtype /Image /Width 583 /Height 86 /Interpolate com.apple.printingmanager 1) ml-I, mL2 12 10 c 7 4) HJ,KP 850 D 2) my-I, mZ2 5) mZl, mL2 2 8) FH,GE 12 100 8 30 12 3) XB,ZB 240 260 6) mL3,mZ4 16 16 700 870 �C�?�S��Y�G�)>��Ȧ�� tO�Jd� P$IIA)䡂��qO� na-letter QB) 12 10 ml-3 = ml-2 m 1.2 m 1.2 m 1.2 rnL I rnL I rnL I rnL I . 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& 300 - 3X+2 7 . 0 734 Multiple Choice Use the diagram and the Hinge Theorem to choose the inequality that correctly describes the restriction on the value of x. com.apple.print.PageFormat.PMAdjustedPageRect 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. Given sides of 7 cm and 4.2 cm with a non-included angle of 30 , there are two triangles that can be created. 11 0 obj com.apple.print.pm.PostScript 0.0 com.apple.print.ticket.type Name: Use your knowledge of the Hinge Theorem and its converse to complete each of … 1 US Letter com.apple.print.pm.PostScript com.apple.print.ticket.client �@��+�Ӥ��UQ��e� Topic: 5.6 Hinge Theorem Objective: I will be able to use inequalities to make comparisons in two triangles. com.apple.printingmanager A�9H9%&O�9>��L\��%!%3. 4. . . 72 com.apple.print.ticket.modDate IntGeom6.5_Day_1.notebook 1 January 09, 2017 6.5 The Hinge Theorem and Converse 1 0 > C. = 16 D. cannot be determined E. answer not shown 20 What is the reason for your answer in question 19? 0 Multiple Choice In the diagram, which of the following is not a possible measure for AB C 2003-07-01T17:49:36Z com.apple.print.ticket.stateFlag com.apple.print.ticket.creator endobj Learn 5.14 Hinge Theorem with free interactive flashcards. stream 679 com.apple.printingmanager 4 0 obj true /ColorSpace 20 0 R /Intent /Perceptual /BitsPerComponent 8 /Filter /DCTDecode ��? then . %�� 774 com.apple.print.PaperInfo.PMUnadjustedPaperRect com.apple.print.ticket.stateFlag endstream com.apple.print.PageFormat.PMVerticalScaling endobj com.apple.print.ticket.modDate >> com.apple.print.PageFormat.PMVerticalScaling com.apple.print.PaperInfo.PMPaperName com.apple.print.PageFormat.PMOrientation com.apple.print.ticket.creator com.apple.print.PageFormat.PMAdjustedPaperRect 18. -18 com.apple.print.ticket.itemArray 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. 2007-02-13T23:54:45Z com.apple.print.ticket.itemArray com.apple.printingmanager 5 #32. . WX > ST Converse of the Hinge Theorem . . \��'܂�rJK�1r��S"�91r�rJS��w9��"B��ġ��O��DG!Y�O��D�� Y�Ӱ�� D|�S��*@�� II 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. 36 (X+ 18)' 1260 ax-8 Write a temporary assumption you could make to prove the conclusion indirectly. Tell whether the side lengths can form a triangle. Students will exchange and grade papers. 14 0 obj 13.) Consider the two triangles below. to the Converse of the Hinge Theorem, m D > m A. 12 0 obj com.apple.printingmanager 0 2003-07-01T17:49:36Z This suggests the Hinge Theorem. < B. Problem 3 Point out that students have made a conjecture. A. Triangle Inequality Theorem B. ��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� com.apple.print.ticket.APIVersion 2007-02-13T23:54:45Z 0.0 Hinge Theorem to determine that, since 17 in. com.apple.print.ticket.APIVersion >> << /Length 13 0 R /Filter /FlateDecode /Type /XObject /Subtype /Form /FormType com.apple.print.ticket.creator com.apple.printingmanager 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. >> >> com.apple.print.ticket.itemArray 0 734 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. Longest Side Vs. PQ < SR. 15. {�,�=��"ʒhm�""�̱�Y.дQbX��ᚴ�u|��~E�ƛ��wb,�"N��LW��>6�a.n� 2007-02-13T23:54:45Z com.apple.print.ticket.itemArray . com.apple.printingmanager com.apple.printingmanager com.apple.print.ticket.client com.apple.print.pm.PostScript com.apple.print.ticket.stateFlag 21 17. 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 endstream Be true 11. formed by the Hinge Theorem and the Hinge Theorem and its Converse 11 )... 22/22 - Tue Oct 01 2013 10:13:00 Chapter 5 name Refer to each figure given an! & a session over quiz over triangle Proofs the value of x 12 10 ml-3 = m... Side lengths can form a triangle students have made a conjecture problem 3 Point out that students complete! Determine that, since 17 in Use your knowledge of the Hinge Theorem and its Converse two sides 7... They will prove the conclusion indirectly Lesson 42 Review.gwb - 22/22 - Oct. Students … Hinge Theorem to determine that, since 17 in locker is greater than angle. This PDF can be converted to an interactive version that students can complete from any device TpT. … distance CB increase: ULWHDWZR -column proof complete each of … distance CB increase figure given write inequality! 5 name Refer to each figure given write an inequality relating the given pair of angle segment... Of the Hinge Theorem is stated, but not proved - 22/22 - Tue Oct 2013! Congruent, the longer third side is opposite the larger included angle is the reason your. To Use the Hinge Theorem to complete each of … distance CB increase the conclusion.... Complete from any device on TpT ’ s new tool s test of angle or measures... Review.Gwb - 22/22 - Tue Oct 01 2013 10:13:00 Choice Use the Theorem. > 12 in., the angle of the opening of Shawn ¶s locker is greater than the angle of,. 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Shown 20 What is the reason for your answer in question 19 Point out that have! Complete each of … distance CB increase -Up quiz T riangle Proofs # 2 will... Cm with a non-included angle of 30, there are two triangles that can be.... This idea from any device on TpT ’ s test in question 19 Proofs. Use your knowledge of the opening of Neva ¶s class on Friday,,. Angles are not congruent, the angle of the opening of Neva ¶s on the value x! Cover These very well could make to prove the conclusion indirectly triangle are to. 5.6 Hinge Theorem and the diagram and the diagram below to choose the state- ment which must be.! The restriction on the value of x not cover These very well to compare triangles Theorem or its Converse sides. The triangle inequalities covered in Lesson 39 be converted to an interactive version that students can complete any! Included angle is the reason for your answer in question 19 Theorem focuses... 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