Geo: 4.6 Triangle congruency by ASA, AAS, HL
 Are these triangles congruent? If so, why?not congruent, not enough infoYes, by AAA ∆≅ thm.Yes, by ASA ∆ ≅ thmYes, by AAS ∆ ≅ thm. ABDC Complete the proof.Given: LM // PO  and  N is the midpoint of LOProve: ∆LMN ≅ ∆OPNN is the midpoint of LO∡LNM ≅ ∡ONP?∆LMN ≅ ∆OPN?Statements∡L ≅ ∡O?LN ≅ ONLM // PO  ?not used: Def. if midpoint?Alternating Interior AnglesASA ∆ ≅ Thm.Vertical Angles?GivenGiven?∡M ≅ ∡P?Reasons Given that AB // CD. Are these triangles congruent?not congruent, not enough infoYes, by AAA ∆≅ thm.Yes, by ASA ∆ ≅ thm.Yes, by SAS ∆ ≅ thm.A▼BE▼DC Are these triangles congruent?Anot congruent, not enough infoYes, HL ∆≅ thm.Yes, by ASA ∆ ≅ thm.Yes, by SAS ∆ ≅ thm.DBC Drag the correct condition that proves the triangle pairscongruent to each other.  HL ∆≅ Thm?Not enough info?SAS ∆ ≅ Thm.?SSS ∆ ≅ Thm.?AAS ∆ ≅ Thm.?ASA ∆ ≅ Thm.?not used: 7.  True or False.     ΔABC ≅ ΔDBC by the HL ≅ theorem.TRUEFALSEACBD 8.  True or False.     ΔABC ≅ ΔDBC by the ASA ≅ theorem.TRUEFALSEA32∘CB32∘D Complete the proof:∡Q and ∡S are right anglesR is the midpoint of QS?Given: R is the midpoint of QS.∡Q and ∡S are right angles.Prove:∆PQR ≅ ∆TSR?∡PRQ ≅ ∡TSR?StatmentsQR ≅ SR?∆PQR ≅ ∆TSRVertical Angles Thm.?Def. of midpointnot used:  ASA ∆ ≅ Thm.?GivenGiven?ReasonsHL ∆≅ Thm.? 10. Drag the correct congruence theorem to the       image that shows how it would be used to prove      the triangles congruent.  For the one that is NOT       used, place it next to the words, "not used".ASA ≅ theorem?HL ≅ theorem?SAS ≅ theorem?AAS ≅ theorem?"not used" What additional information is needed in order to prove thesetriangles are congruent by AAS?SU ≅ HFTU ≅ GF∡U ≅ ∡F∡T ≅ ∡G Are these triangles congruent?  If not why not?Yes, Congruent by AASYes, Congruent by ASAYes, Congruent by SSSNo, not congruent, AAA doesnot prove triangles congruent.  What additional information is needed in order to prove thesetriangles are congruent by HL?SU ≅ HFTU ≅ GF∡U ≅ ∡F∡T ≅ ∡G What additional information is needed in order to prove thesetriangles are congruent by AAS?SU ≅ HFTU ≅ GF∡U ≅ ∡F∡T ≅ ∡G
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