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Using Two Pairs of Congruent Triangles in a Proof
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D C B A E Prove: CE DE 1.AEB, AC AD, 1. Given BC BD 1) 2. AB AB2. Reflexive 3. ACB ADB3. SSS SSS 4. CAE DAE4. CPCTC 5. AE AE5. Reflexive 6. ACE ADE6. SAS SAS 7. CE DE7. CPCTC
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N I V E K Prove: NE bisects KV 1.NK NV, 1. Given IK IV 2) 2. IN IN 2. Reflexive 3. KIN VIN 3. SSS SSS 4. <KNE <VNE4. CPCTC 5. NE NE5. Reflexive 6. KEN VEN 6. SAS SAS 7.KE VE7. CPCTC 8.NE bisects KV8. A segment is bisected if it is cut in half. Plan:
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C AB E D F G 1.AD CB, DC BA 1. Given EF bisects BD Prove: FG EG 3) 5. DG BG 5. A bisector cuts in half 2.BD BD2. Reflexive 3. ABD CDB3. SSS SSS 4. CDB ABD 4. CPCTC 6. DGE BGF6. Vertical Angles are congruent 7. DGE BGF7. ASA ASA 8. FG EG8. CPCTC
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Q A D C B P 21 Prove: QB QD 1. 1 2, AP CP 1. Given PQ, PAB, PCD, AQD, CQB 2.PQ PQ 2. Reflexive 3. PAQ PCQ 3. SAS SAS 4.QA QC 4. CPCTC QAP QCP 5. BAQ is suppl to QAP 5. Linear pairs are DCQ is suppl. to PCQ supplements. 6. BAQ DCQ 6. It 2 <‘s are , then their suppelments are 7. BQA DQC 7. Vertical <‘s are 8. PAQ PCQ 8. ASA ASA 9. QB QD 9. CPCTC
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Homework: Pairs of Congruent Triangles D E C G A FB Prove: GE GF 1.AC and BD bisect1. Given each other at G, EGF 1) 2. AG CG, BG DG2. A bisector cuts in half 3. AGB CGD3. Vertical ’s are 4. AGB CGD4. SAS SAS 5. A C5. CPCTC 6. AGF CGE6. Vertical ’s are 7. AGB CGD 7. ASA ASA 8. GE GF8. CPCTC
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2) B C A D 1E 2 Prove: 1 2 1.AC AD, BC BD1. Given AB intersects CD at E 2.AB AB2. Reflexive 3. ABC ABD3. SSS SSS 4. CAB DAB4. CPCTC 5. ACE ADE5. If 2 sides of a are , then opposite ’s are 6. ADE ACE6. ASA ASA 7. 1 22. CPCTC
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3) T PQ R S 1.RP RQ, SP SQ1. Given Prove: RT bisects PQ 2. RS RS2. Reflexive 3. RPS RQS3. SSS SSS 4. PRS QRS4. CPCTC 5. RPT RQT5. If 2 sides of a are , then opposite ’s are 6. RPT RQT6. ASA ASA 7. PT QT7. CPCTC 8.RT bisects PQ8. A segment is bisected if its cut in half
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