Transcription of Given: ABC CD bisects AB CD AB Prove: ACD BCD
1 #1. given : ABC. CD bisects AB. CD AB. prove : ACD BCD. Statement Reasons 1. ABC 1. given CD bisects AB. CD AB. 2. AD DB Side 2. A bisector cuts a segment into 2. parts. 3. CDA and CDB are right 3. lines form right . 4. CDA CDB Angle 4. All rt are . 5. CD CD Side 5. Reflexive post. 6. ACD BCD 6. SAS SAS. #2. given : ABC and DBE bisect each other. prove : ABD CBD. Statement Reasons 1. ABC and DBE bisect each other. 1. given 2. AB BC Side 2. A bisector cuts a segment into 2. BD BE Side parts. 3. ABD and BEC are vertical 3. Intersecting lines form vertical . 4. ABD BEC Angle 4. Vertical are . 5. ABD CBD 5. SAS SAS. #1. #3. given : AB CD and BC DA. DAB, ABC, BCD and CDA. are rt . prove : ABC ADC. Statement Reasons 1. AB CD Side 1. given BC DA Side 2. DAB, ABC, BCD and CDA 2. given are rt . 3.
2 ABC ADC Angle 3. All rt are . 4. ABC ADC 4. SAS SAS. #4. given : PQR RQS. PQ QS. prove : PQR RQS. Statement Reasons 1. PQR RQS Angle 1. given PQ QS Side 2. RQ RQ Side 2. Reflexive Post. 3. PQR RQS 3. SAS SAS. #1. #5. given : AEB & CED intersect at E. E is the midpoint AEB. AC AE & BD BE. prove : AEC BED. Statement Reasons 1. AEB & CED intersect at E 1. given E is the midpoint AEB. AC AE & BD BE. 2. AEC and BED are vertical 2. Intersecting lines form vertical . 3. AEC BED Angle 3. Vertical are . 4. AE EB Side 4. A midpoint cut a segment into 2. parts 5. A & B are rt. 5. lines form right . 6. A B Angle 6. All rt are . 7. AEC BED 7. ASA ASA. #6. given : AEB bisects CED. AC CED & BD CED. prove : EAC EBD. Statement Reasons 1. AEB bisects CED 1. given AC CED & BD CED. 2. CE ED Side 2. A bisector cuts an angle into 2 parts.
3 3. ACE & EDB are rt 3. Lines form rt . 4. ACE EDB Angle 4. All rt are . #1. 5. AEC & DEB are vertical 5. Intersect lines form vertical . 6. AEC DEB Angle 6. Vertical are . 7. EAC EBD 7. ASA ASA. #7. given : ABC is equilateral D midpoint of AB. prove : ACD BCD. Statement Reasons 1. ABC is equilateral 1. given D midpoint of AB. 2. AC BC Side 2. All sides of an equilateral are . 3. AD DB Side 3. A midpoint cuts a segment into 2 parts. 4. CD CD Side 4. Reflexive Post 5. ACD BCD 5. SSS SSS. #8. given : m A = 50, m B = 45, AB = 10cm, m D = 50. m E = 45 and DE = 10cm prove : ABC DEF. Statement Reasons 1. m A = 50, m B = 45, 1. given AB = 10cm, m D = 50. m E = 45 and DE = 10cm 2. A = D Angle and 2. Transitive Prop B = E Angle AB = DE Side 3. ASA ASA. 3. ABC DEF. #1. #9. given : GEH bisects DEF.
4 M D = m F. prove : GFE DEH. Statement Reasons 1. GEH bisects DEF 1. given m D = m F Angle 2. DE EF Side 2. Bisector cut a segment into 2 . parts. 3. 1 & 2 are vertical 3. Intersect lines form vertical . 4. 1 2 Angle 4. Vertical are . 5. GFE DEH 5. ASA ASA. #10. given : PQ bisects RS at M. R S. prove : RMQ SMP. Statement Reasons 1. PQ bisects RS at M 1. given R S Angle 2. RM MS Side 2. Bisector cut a segment into 2 . #1. parts 3. 1 & 2 are vertical angles 3. Intersect lines form vertical . 4. 1 2 Angle 4. Vertical are . 5. RMQ SMP 5. ASA ASA. #11. given : DE DG. EF GF. prove : DEF DFG. Statement Reasons 1. DE DG Side 1. given EF GF Side 2. DF DF Side 2. Reflexive Post 3. DEF DFG 3. SSS SSS. #12. given : KM bisects LKJ. LK JK. prove : JKM LKM. Statement Reasons 1. KM bisects LKJ 1. given LK JK Side 2.
5 1 2 Angle 2. An bisectors cuts the into 2 parts #1. 3. KM KM Side 3. Reflexive Post 4. JKM LKM 4. SAS SAS. #13. given : . PR QR. P Q. RS is a median prove : PSR QSR. Statement Reasons 1. PR QR Side 1. given P Q Angle RS is a median Side 2. PS SQ 2. A median cuts the side into 2 parts 3. PSR QSR 3. SAS SAS. #14. given : EG is bisector EG is an altitude prove : DEG GEF. Statement Reasons 1. EG is bisector 1. given EG is an altitude 2. 3 4 Angle 2. An bisector cuts an into 2 parts. #1. 3. EG DF 3. An altitude form lines. 4. 1 & 2 are rt 4. lines form right angles. 5. 1 2 Angle 5. All right angles are . 6. GE GE Side 6. Reflexive Post 7. DEG GEF 7. ASA ASA. #15. given : A and D are a rt . AE DF. AB CD. prove : EC FB. Statement Reasons 1. A and D are a rt 1. given AE DF Side AB CD. 2. A D Angle 2.
6 All right angles are . 3. BC BC 3. Reflexive Post. 4. AB + BC CD + BC 4. Addition Prop. or AC BD Side 5. AEC DFB 5. SAS SAS. 6. EC FB 6. Corresponding parts of are . #16. given : CA CB. D midpoint of AB. prove : A B. Statement Reasons 1. CA CB Side 1. given D midpoint of AB. #1. 2. AD DB Side 2. A midpoint cuts a segment into 2 parts 3. CD CD Side 3. Reflexive Post 4. ADC DBC 4. SSS SSS. 5. A B 5. Corresponding parts of are . #17. given : . AB CD. CAB ACD. prove : AD CB. Statement Reasons 1. AB CD Side 1. given CAB ACD Angle 2. AC AC Side 2. Reflexive Post 3. ACD ABC 3. SAS SAS. 4. AD CB 4. Corresponding parts of are . #18. given : AEB & CED bisect each Other prove : C D. Statement Reasons 1. AEB & CED bisect each other 1. given 2. CE ED Side & AE EB Side 2. A bisector cuts segments into 2 parts.
7 3. 1 and 2 are vertical 3. Intersect lines form vertical . #1. 4. 1 2 Angle 4. Vertical are . 5. AEC DEB 5. SAS SAS. 6. C D 6. Corresponding parts of are #19. given : KLM & NML are rt . KL NM. prove : K N. Statement Reasons 1. KLM & NML are rt 1. given KL NM Side 2. KLM NML Angle 2. All rt are . 3. LM LM Side 3. Reflexive Post. 4. KLM LNM 4. SAS SAS. 5. K N 5. Corresponding parts of are . #20. given : AB BC CD. PA PD & PB PC. prove : a) APB DPC. b) APC DPB. Statement Reasons 1. AB BC CD Side 1. given PA PD Side & PB PC Side 2. ABP CDP 2. SSS SSS. 3. APB DPC 3. Corresponding parts of are . #1. 4. BPC BPC 4. Reflexive Post. 5. APB + BPC DPC + BPC 5. Addition Prop. or APC DPB. #21. given : PM is Altitude PM is median prove : a) LNP is isosceles b) PM is bisector Statement Reasons 1. PM is Altitude & PM is median 1.
8 given 2. PM LN 2. An altitude form lines. 3. 1 and 2 are rt 3. lines form right angles. 4. 1 2 4. All right angles are . 5. LM MN 5. A median cuts the side into 2 parts 6. PM PM 6. Reflexive Post. 7. LMP PMN 7. SAS SAS. 8. PL PN 8. Corresponding parts of are . 9. LNP is isosceles 9. An Isosceles is a with2 sides 10. LPN MPN parts of are . 11. PM is bisector 11. A bisector cuts an into 2 parts #22. #1. given : CA CB. prove : CAD CBE. Statement Reasons 1. CA CB 1. given 2. 2 3 2. If 2 sides are then the opposite are . 3. 1 & 2 are supplementary 3. Supplementary are form by a 3 & 4 are supplementary linear pair. 4. 1 4 or CAD CBE 4. Supplement of are . #23. given : AB CB & AD CD. prove : BAD BCD. Statement Reasons 1. AB CB & AD CD 1. given 2. 1 2 2. If 2 sides are then the opposite 3 4 are.
9 3. 1 + 3 2 + 4 3. Addition Post. or BAD BCD. #24. #1. given : ABC DEF. M is midpoint of AB. N is midpoint DE. prove : AMC DNF. Statement Reasons 1. ABC DEF 1. given 2. M is midpoint of AB 2. given N is midpoint DE. 3. D A Angle and DF AC Side 3. Corresponding parts of are . 4. AM MB and DN NE Side 4. A midpoint cuts a segment into 2 parts 5. AMC DNF 5. SAS SAS. #25. given : ABC DEF. CG bisects ACB. FH bisects DFE. prove : CG FH. Statement Reasons 1. ABC DEF. CG bisects ACB. FH bisects DFE. #1. #26. given : AME BMF. DE CF. prove : AD BC. Statement Reasons 1. AME BMF 1. given DE CF. 2. EM MF 2. Corresponding parts of are . AM MB Side 1 2 Angle 3. DE + EM CF + MF 3. Addition Post. or DM MC Side 4. ADM BCM 4. SAS SAS. 5. AD BC 5. Corresponding parts of are . given : AEC & DEB bisect each other prove : E is midpoint of FEG.
10 Statement Reasons 1. AEC & DEB bisect each other 1. given #1. 2. DE BE Side and AE EC Side 2. A bisector cuts a segment into 2 parts. 3. AEB & DEC are vertical 3. Intersecting lines form vertical . 4. AEB DEC Angle 4. Vertical are . 5. AEB DEC 5. SAS SAS. 6. D B 6. Corresponding parts of are . 7. 1 & 2 are vertical angles 7. Intersecting lines form vertical . 8. 1 2 8. Vertical are . 9. GEB DEF 9. ASA ASA. 10. GE FE 10. Corresponding parts of are . 11. E is midpoint of FEG 11. A midpoint divides a segment into 2 parts. #28. given : BC BA. BD bisects CBA. prove : DB bisects CDA. Statement Reasons #1. 1. BC BA Side 1. given BD bisects CBA. 2. 1 2 Angle 2. A bisector cuts an angle into 2 parts. 3. BD BD Side 3. Reflexive Post. 4. ABD BCD 4. SAS SAS. 5. 3 4 5. Corresponding parts of are.
