Geo: 4.6 Triangle congruency by ASA, AAS, HL

Are these triangles congruent? If so, why? not congruent, not enough info Yes, by AAA ∆≅ thm. Yes, by ASA ∆ ≅ thm Yes, by AAS ∆ ≅ thm. A B D C Complete the proof. Given: LM // PO and N is the midpoint of LO Prove: ∆LMN ≅ ∆OPN N is the midpoint of LO ∡LNM ≅ ∡ONP ? ∆LMN ≅ ∆OPN ? Statements ∡L ≅ ∡O ? LN ≅ ON LM // PO ? not used: Def. if midpoint ? Alternating Interior Angles ASA ∆ ≅ Thm. Vertical Angles ? Given Given ? ∡M ≅ ∡P ? Reasons Given that AB // CD. Are these triangles congruent? not congruent, not enough info Yes, by AAA ∆≅ thm. Yes, by ASA ∆ ≅ thm. Yes, by SAS ∆ ≅ thm. A ▼ B E ▼ D C Are these triangles congruent? A not congruent, not enough info Yes, HL ∆≅ thm. Yes, by ASA ∆ ≅ thm. Yes, by SAS ∆ ≅ thm. D B C 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. TRUE FALSE A C B D 8. True or False. ΔABC ≅ ΔDBC by the ASA ≅ theorem. TRUE FALSE A 32 ^{∘}C B 32 ^{∘}D Complete the proof: ∡Q and ∡S are right angles R is the midpoint of QS ? Given: R is the midpoint of QS.∡Q and ∡S are right angles. Prove: ∆PQR ≅ ∆TSR ? ∡PRQ ≅ ∡TSR ? Statments QR ≅ SR ? ∆PQR ≅ ∆TSR Vertical Angles Thm. ? Def. of midpoint not used: ASA ∆ ≅ Thm. ? Given Given ? Reasons HL ∆≅ 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 these triangles are congruent by AAS? SU ≅ HF TU ≅ GF ∡U ≅ ∡F ∡T ≅ ∡G Are these triangles congruent? If not why not? Yes, Congruent by AAS Yes, Congruent by ASA Yes, Congruent by SSS No, not congruent, AAA does not prove triangles congruent. What additional information is needed in order to prove thesetriangles are congruent by HL? SU ≅ HF TU ≅ GF ∡U ≅ ∡F ∡T ≅ ∡G What additional information is needed in order to prove these triangles are congruent by AAS? SU ≅ HF TU ≅ GF ∡U ≅ ∡F ∡T ≅ ∡G |

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