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4.2 Triangle Congruence SSS and SAS November 18, 2014 Nov 188:38 AM D.I.R.T? 1) Given figure DEFG NSTP, list all the congruent parts. Given figures MNOW BDCR, fill in the blanks. M 10 N D C 100 O 15 W B R 2) BD=_________ 3) m<C=__________ 4) MW ________ 5) m<M=__________ 6) <R ________ 7) OW= ___________ Nov 188:28 AM 1 4.2 Triangle Congruence SSS and SAS November 18, 2014 Find the missing variable. Nov 610:07 AM 4.2 Triangle Congruence by SSS and SAS Objective: To prove two triangles congruent using the SSS and SAS Postulates Postulate 41 SideSideSide (SSS) If three sides on one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Q H G F P R ~ GHF = PQR Nov 188:29 AM 2 4.2 Triangle Congruence SSS and SAS November 18, 2014 The word included used frequently when referring to angles and side of a triangle. A Given the two sides, what is the included angle? AC and AB AC and CB _____________ <B is included by which two sides? _________ Given the two angles, what is the included side? <A and <B ______________ C <B and <C _____________ B AC is the included side for which two angles? ______________ Nov 188:32 AM Postulate 42 SideAngleSide (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Q H G F P R ~ GHF = PQR Nov 188:38 AM 3 4.2 Triangle Congruence SSS and SAS November 18, 2014 What other information, if any, do you need to prove the two triangles are congruent by SSS or SAS? A D C B E Given: AC and BD bisect each other A D C B E Nov 188:41 AM ~ ~ Given: AB = CB, AD = CD ~ Proove: ABD = CBD B A C Which Postulate can we use, if any, to prove that the two triangle are congruent? D Nov 188:43 AM 4 4.2 Triangle Congruence SSS and SAS November 18, 2014 ~ Given: AB = CB, BD bisects <B ~ Proove: ABD = CBD B Which Postulate can we use, if any, to prove that the two triangle are congruent? A C D Nov 188:45 AM ~ Given: JA // SY, JA = SY Prove the triangles are =~ A J S Y Nov 188:46 AM 5 4.2 Triangle Congruence SSS and SAS November 18, 2014 Tell whether the triangles are congruent. If so, justify and write a congruence statement. ex 3) J < Y ex 4) U < Know: Found: L M A Know: < < H T Found: Nov 188:47 AM 6