1 2 GEOMETRY Worksheet ≅∆s Worksheet II NAME___________________________________ DATE______________________ PERIOD______ Write ∆ congruence (if possible) and tell which postulate (SSS, SAS, ASA, or AAS) you are using. 1. ∆GKM≅∆__________ by __________ 2. ∆ABC≅∆__________ by __________ G GK ML GK≅ML K M L 4. ∆KLG≅∆__________ by __________ P G GL bisects KM GL bisects ∠KGM S R E C B 3. ∆PRQ≅∆__________ by __________ R is midpoint of both PT and QS D A B ≅ E C is midpoint of BE ∠DCB≅∠ECA Q T K 5. ∆RNG≅∆__________ by __________ L 6. ∆DAB≅∆__________ by __________ N RN ≅ NE ∠R ≅ ∠E A AB DC ∠A ≅ ∠C A D E 7. ∆WIT≅∆__________ by __________ W T is midpt. of HI WI HC B G S R M C 8. ∆CON≅∆__________ by __________ CO ≅ GC ON ≅ NG I T O C N G C H 9. ∆GEO≅∆__________ by __________ 10. ∆TES ≅∆__________ by __________ OG bisects ∠EOM EO ≅ MO E is midpoint of both TA and SX TS ≅ AX E G O T E X S M A 3 11. ∆DEB≅∆__________ by __________ 12. ∆KEG≅∆__________ by __________ C DE ≅ EC BE ≅ AE D E is midpoint of KW ∠KEG ≅ ∠WEH G ∠K ≅ ∠W E H B K A 13. ∆TVU≅∆__________ by __________ W 14. ∆MDB ≅∆__________ by __________ T ∠VTU ≅ ∠UVW ∠ TVU ≅ ∠UWV E V D is midpoint of MT BD ≅ ZT BD ZT U Z B M D T W 15. ∆WUY≅∆__________ by __________ 16. ∆BAD≅∆__________ by __________ V U is midpoint of both YX and WV WY ≅ VX AD bisects ∠BAC BA ≅ CA X U C D A B W Y 17. ∆PFS≅∆__________ by __________ 18. ∆AED≅∆__________ by __________ P FP ≅ HP RF ≅ SH R S F 19. ∆COL≅∆__________ by __________ ∆COU≅∆__________ by __________ A L D AB DC AD BC B U C F 20. ∆ABD≅∆__________ by __________ C O B E D H ∠CUD ≅ ∠CLO CU≅CL ∠OCU≅∠DCL A AE ≅ FC DE ≅ FB ∠BED ≅ ∠DFB D 4 C 5 Geometry Worksheet-Congruent Triangles III Name___________________________________ Date_________________________Period______ Label the drawing with the given information and state why the triangles are congruent. Use all eight theorems (SSS, SAS, ASA, AAS, HA, HL, LL, LA) 1. ∆POR ≅ ∆_________ by ________ ∠POR ≅ ∠TOR PO ≅ TO P 2. ∆LFE ≅ ∆_________ by ________ LF is the ⊥ bisector of ET O R T L E F 3. ∆PNO ≅ ∆_________ by ________ 4. ∆HOM ≅ ∆_________ by ________ N is the midpoint of OE P PN ≅ HE HM bisects ∠OHE ∠O ≅ ∠E H T H PO ⊥ ON HN ⊥ NE O O E E N M 5. ∆MIT ≅ ∆_________ by ________ 6. ∆RUJ ≅ ∆_________ by ________ I ≅ E JR⊥ UY JR bisects ∠UJY J TI ME T I E M U R 7. ∆XTE ≅ ∆_________ by ________ 8. ∆NEW ≅ ∆_________ by ________ X is the midpoint of both TS and AE NW ⊥ NE SW ⊥ SE ∠NEW ≅ ∠SEW T A E W X E N S 6 Y S 9. ∆PTC ≅ ∆_________ by ________ ∠T ≅ ∠I ∠TPC ≅ ∠PCI 10. ∆TUH ≅ ∆_________ by ________ P H HU bisects ∠OHT UH bisects ∠OUT I O T T C U 11. ∆MAO ≅ ∆_________ by ________ 12. ∆NOC ≅ ∆_________ by ________ MA ⊥ OA A is the midpoint of MR O C CO ≅ NE CN ≅ OE M O A N E R 13. ∆ULP ≅ ∆_________ by ________ PL bisects ∠UPA LP bisects ∠ALU P 14. ∆HRO ≅ ∆_________ by ________ A U L 15. ∆DGI ≅ ∆_________ by ________ DG ≅ ER NE ≅ IG DG ⊥ NI RE ⊥ NI D M O E 16. ∆ANY ≅ ∆_________ by ________ I E G N H HR ⊥ RE ME ⊥ ER O is the midpoint of RE ∆HMO is isos. with base HM R R YA ⊥ AK SK ⊥ KA N is the midpoint of YS Y A K N S 7 Geometry Proofs using Isosceles Triangles 1. Given: Prove: Name__________________________________ Date______________________Period_______ ∠3 ≅ ∠4 MA ≅ MC M 3 1 A 4 C 2 C 2. Given: Prove: ∆CAN is an isosceles triangle with vertex ∠N CA || BE ∆NEB is an isosceles triangle. 1 2 B 3 E 4 N G F 3. Given: Prove: 5 ∠5 ≅ ∠6 FR ≅ GS ∠4 ≅ ∠3 3 4 1 X 6 2 R S B 4. Given: Prove: ∠3 ≅ ∠4 ∠1 ≅ ∠2 ∆ABC is isosceles with base AC 1 2 E 3 A 4 C C 5. Given: Prove: CA ≅ CB ∠1 ≅ ∠2 AQ ≅ BP 1 A 8 P 2 Q B A Geometry Pre AP CPCTC Proofs Worksheet I CPCTC: Corresponding Parts of Congruent Triangles are Congruent Use one of the congruence theorems we have studied (SSS, SAS, AAS, ASA) to prove that the triangle are congruent. Then use CPCTC to help draw further conclusions. Your answers should be in flow proof format. B 1. Given: BD ⊥ AC D is the midpoint of AC Prove: ∠A ≅ ∠C A C D E G Given: ∠E ≅ ∠P K is the midpoint of EP Prove: EG ≅ MP 2. K P M 3. R T Given: RT WQ ∠R ≅ ∠Q Prove: RW ≅ TQ Q W B 4. Given: ∠A ≅ ∠C ∠1 ≅ ∠2 Prove: BD bisects ∠ADC 1 2 A C 3 4 D 5. E G Given: H is the midpoint of GM H is the midpoint of EK Prove: EG MK H M K 9 Geometry Pre AP CPCTC Proofs Worksheet II Use one of the congruence theorems we have studied (SSS, SAS, ASA, AAS, HA, HL, LL, LA) to prove that the triangle are congruent. Then use CPCTC to help draw further conclusions. Your answers should be in flow proof A format. 1. Given: Prove: CA≅RA CS≅RS ∠ CHR≅ ∠ RIC H I S 1 2 C 2. R Given: WR ≅ ST WT ≅ SR Prove: WT SR R W T 3. S Given: AB EG B A C AB ≅ EG ∠A ≅ ∠G Prove: AD ≅ GC D G E H 4. K Given: ∠H ≅ ∠W P is the midpoint of HW Prove: HW bisects KQ P Q 5. 6. W B Given: AB ≅ BC ∠A ≅ ∠C Prove: ∠AEB ≅ ∠CDB E D A Given: QP ⊥ PT C Q ST ⊥ PT QP ≅ ST ∠Q ≅ ∠S S M Prove: M is the midpoint of PT 10 P T
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