SSS, SAS, ASA Proofs

Geometry/Trig Name __________________________ Unit 4 Proving Triangles Congruent Packet Date ___________________________ #1 Given: LF || WH; HY  LY Prove: ΔWHY  ΔFLY F H Y L W Statements Reasons #2 M Given: MH || AT; MH  AT Prove: ΔMAH  ΔTHA H Statements #3 Given: T Reasons W ZX bisects WZY ZX bisects WXY Prove: A Z X ΔZYX  ΔZWX Statements Y Reasons #4 A Given: E is the midpoint of AD E is the midpoint of BC Prove: ΔAEB  ΔDEC C E B D Statements 1. _________________________________ Reasons 1. __________________________________ 2. _________________________________ 2. __________________________________ 3. _________________________________ 3. 4. _________________________________ 4. __________________________________ 5. _________________________________ 5. 6. _________________________________ 6. __________________________________ Given Vertical Angles are Congruent #5 A Given: AC  BD B  D Prove: ΔACB  ΔACD B D C Statements Reasons #6 M Given: MO  NP MN  MP Prove: ΔMON  ΔMOP N Statements 1. O P Reasons _________________________________ 1. __________________________________ 2. _________________________________ 2. 3. _________________________________ 3. 4. _________________________________ 4. 5. _________________________________ 5. 6. _________________________________ 6. __________________________________ Definition of Perpendicular Lines __________________________________ Given __________________________________ #7 W Given: WO  ZO; XO  YO Prove: W  Z Z O X Statements Y Reasons Q #8 Given: PR bisects QPS and QRS Prove: RQ  RS R P S Statements #9 A Given: AC  BD; AD  DC B Prove: AB  BC Statements C Reasons D Reasons #10 Y Given: ZW || YX; ZW  XY Prove: ZY || WX 4 X Z 2 1 3 W Statements Reasons 1. _________________________________ 1. _________________________________ 2. _________________________________ 2. If lines are parallel, then alternate interior angles are congruent. 3. _________________________________ 3. _________________________________ 4. _________________________________ 4. _________________________________ 5. 5. _________________________________ ΔXYZ  ΔZWX 6. _________________________________ 6. CPCTC 7. _________________________________ 7. _________________________________ _________________________________ S #11 Given: P  S O is the midpoint of PS Prove: Q P Statements 1. O O is the midpoint of RQ P  S, O is the midpoint of PS 1. R Reasons __________________________________ 2. __________________________________ 2. __________________________________ 3. __________________________________ 3. 4. __________________________________ 4. __________________________________ 5. 5. __________________________________ RO  QO 6. __________________________________ Vertical Angles are Congruent 6. __________________________________ J #12 Given: JK  KM, JL  ML Prove: KL bisects JKM K L M Statements Reasons JK  KM, JL  ML 1. __________________________________ 2. __________________________________ 2. __________________________________ 3. __________________________________ 3. __________________________________ 4. __________________________________ 4. 5. __________________________________ 5. __________________________________ 1. CPCTC Mixed Proofs Practice Directions: Complete the proofs on a separate piece of paper. Mark diagrams as necessary. 2) Given: 1) Given: AB || DE; AB  ED AB || CD; AD || CB Prove: Prove: ΔABM  ΔEDM A ΔABC  ΔCDA B B 4 3 M 2 D E D 4) Given: X and Y are right angles; XZ  YZ M Prove: ΔLMO  ΔNMO 1 A 3) Given: MO bisects LMN L and N are right angles W Prove: ΔWXZ  ΔWYZ L N X O 5) Given: Y Z C is the midpoint of AE 6) Given: AB  CB, AD  CD C is the midpoint of BD Prove: C Prove: A  C B AB || ED A B C D E 7) Given: MT bisects ATH, AT  HT 8) Given: Prove: Prove: MT bisects AMH C BC || AD, A  C BC  AD B A M D A C T H A D