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G.CO,8 STUDENT NOTES & PRACTICE WS #7 - geometrycommoncore.com DOES SSS ESTABLISH TRIANGLE CONGRUENCE? YES!!! AABC = AWER (SSS) k.fr. "P" AABD = ACBD (SSSI ATHJ = ARJH DOES SAS ESTABLISH TRIANGLE-CONGRUENCE? YES!!! AGHK = AGFK (SAS) or (SSS) AABC = AUYM (SAS) AABC = AHBM (SAS) DOES ASA ESTABLISH TRIANGLE CONGRUENCE? YES!!! ABTG = AETG {AsA) AGTE = AGYD (AsA) ATEG = AULK {ASA) DOES AAS/SAA ESTABLISH TRIANGTE CONGRUENCE? YES!!! this is a special form of ASA. In any triangle, if you have two angles you are able to determine the third angle because they sum to 180o. So by knowing two angles, you actually know three angles. So ASA and AAS/SAA both work as congruence relationships. Yes, ANGLE-SIDE-ANGLE Third Angles are Congruent. ANGLE-ANGTE.SIDE G.CO.8 STUDENT NOTES & PRACTICE WS #7 - geometrycommoncore.com 2 RUENCE? SOMETIMES..... This is a difficult case.... it sometimes produces congruence and other times it doesn't. We will look at each case to see when it works and when it doesn't. CASE #L- AS1S2, when Sz is greater than Sr. This forms a triangle congruence relationship. There is only one way for be placed to complete the triangle. CASE #2 - ASrSz, when Sz Sz to is less than 51. (Too Short) This is a weird case but when establishing all things that could happen we need to include this. lt is possible that Sz is not long enough to close the triangle. This of course is not a congruence relationship, it doesn't even form a triangle. CASE #3 - ASrSz, when Sz is less than Sr (1 lntersection) - This case is typically known as HL, which stands for Hypotenuse Leg. tt gets this special name because it is the right triangle that locks this shape. A way to understand why this forms a congruence relationship is because in a right triangle if you know two sides, you can use the Pythagorean Theorem to calculate the third side. Now you have SSS or SAS, which we have already established to be congruence criteria. HL forms a triangle congruence relationship. CASE #4 - ASrSz, when Sz ,t' I, ,t' I, is less than Sr. (2 lntersections) This is known as the AMBIGIOUS CASE because two different triangles can be formed by this information. Because 52 is shorter it can swing to form two possiblelocations.ThisdoesNoTformatrianglecongruencerelationship.il,, N}"IIS (Now You Trv Somel 1. Are the following pairs of triangles congruent? <1 €v lf they arg.then name their congruence criteria. (SSS, SAS, ASA, AAS, HL or AS1S2 (Sz > Sr)) a)yes6r- o)@/*o 5AS- .@/rvo SSS- ar@ruo tA(S geometrycommoncore.com G'co.8 sruDENT NoTEs & pRAcrtcE ws #r z 2' Are the following pairs of triangle congruent? yEs, lf create a congruence statement and name the congruence criteria (SS$ SAS, ASA, AAS, HL or AS1S2 (Sz > Sr)). @z*o a) A-EDC _=A_HNC criteria AIS/S @/ b) A_C t* ruo eD = A_CE R ftSA criteria cED =A_E!T ^ s.A6 Criteria d) @z *o A_lr-Dc_ = [ KLP{ Criteria A e) Criteria ves l Se (1-o\ Sz)Sr .k"