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2.5ExploringCongruentTriangles.notebook October 30, 2012 Section 2.5 Exploring Congruent Triangles Goal: Determine the minimum amount of information needed to prove that two triangles are congruent. May 910:17 AM 1 2.5ExploringCongruentTriangles.notebook October 30, 2012 Two shapes are congruent if all sides and angles in one, are equal to the sides and angles in the other. Oct 2812:38 PM 2 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:30 PM 3 2.5ExploringCongruentTriangles.notebook October 30, 2012 Name the corresponding sides and angles of the following triangles. Are the triangles congruent? Oct 2812:59 PM 4 2.5ExploringCongruentTriangles.notebook October 30, 2012 ΔABC ΔPQR Oct 2812:50 PM 5 2.5ExploringCongruentTriangles.notebook October 30, 2012 Identify the congruent parts of the following triangles. Write the congruency statement, if possible. = = = Oct 2812:50 PM 6 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:53 PM 7 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:20 PM 8 2.5ExploringCongruentTriangles.notebook October 30, 2012 X is If I told you that the measure of 65°, and nothing else, is there only one triangle you could draw? Jun 2210:39 AM 9 2.5ExploringCongruentTriangles.notebook October 30, 2012 If I told you that the length of YZ is 2.74 m, and nothing else, is there only one triangle you could draw? Jun 2210:52 AM 10 2.5ExploringCongruentTriangles.notebook October 30, 2012 What if I gave you two pieces of information? What if I gave you three pieces of information? Jun 2210:53 AM 11 2.5ExploringCongruentTriangles.notebook October 30, 2012 There are minimum sets of angle and side measurements that, if known, allow you to conclude that two triangles are congruent. Oct 281:18 PM 12 2.5ExploringCongruentTriangles.notebook October 30, 2012 CONGRUENCE POSTULATES (SSS) Side - Side - Side Postulate If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. SSS EXAMPLES http://www.mathopenref.com/congruentsss.html Oct 281:31 PM 13 2.5ExploringCongruentTriangles.notebook October 30, 2012 (SAS) Side - Included Angle - Side Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. The included angle is the one that is between the two known sides. SAS EXAMPLES http://www.mathopenref.com/congruentsas.html Oct 281:32 PM 14 2.5ExploringCongruentTriangles.notebook October 30, 2012 (ASA) Angle - Included Side - Angle Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. http://www.mathopenref.com/congruentasa.html Oct 281:33 PM 15 2.5ExploringCongruentTriangles.notebook October 30, 2012 (AAS) Angle - Angle - Not Included Side Postulate If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent. http://www.mathopenref.com/congruentaas.html Oct 281:33 PM 16 2.5ExploringCongruentTriangles.notebook October 30, 2012 Congruent Triangles - Why SSA doesn't work http://www.mathopenref.com/congruentssa.html Congruent Triangles - Why AAA doesn't work http://www.mathopenref.com/congruentaaa.html Oct 281:35 PM 17 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:24 PM 18 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:24 PM 19 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:46 PM 20 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:12 PM 21 2.5ExploringCongruentTriangles.notebook October 30, 2012 Are the following triangles congruent? Why or why not? If the triangles are congruent, state the congruence statement. Oct 2812:07 PM 22 2.5ExploringCongruentTriangles.notebook October 30, 2012 Are the following triangles congruent? Why or why not? If the triangles are congruent, state the congruence statement. Oct 2812:07 PM 23 2.5ExploringCongruentTriangles.notebook October 30, 2012 Are the following triangles congruent? Why or why not? If the triangles are congruent, state the congruence statement. Oct 2812:08 PM 24 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:41 PM 25 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:25 PM 26 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:25 PM 27 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:26 PM 28 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:27 PM 29 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:28 PM 30 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:29 PM 31 2.5ExploringCongruentTriangles.notebook October 30, 2012 Oct 2812:29 PM 32 2.5ExploringCongruentTriangles.notebook October 30, 2012 If the triangles are congruent, state the congruence statement. Oct 253:45 PM 33 2.5ExploringCongruentTriangles.notebook October 30, 2012 2.5 Assignment: Nelson Foundations of Mathematics 11, Sec 2.5, pg, 106 Questions: 1 ‐ 4 Jun 228:40 AM 34