Pre-Calculus Homework Solutions 176

Pre-Calculus Homework Solutions 176 - 33 Given ABC PQR BD...

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Unformatted text preview: 33. Given: ABC PQR, BD is an altitude of ABC. QS is an altitude of PQR. QP 36. Given: RU bisects VU RT QS BD Prove: BA S Prove: VV R U V A CP D R R S QP ABD PQS by AA Similarity and BA by definition of similar polygons. 34. Given: C BDA Statements QS BD SRT. 1. Given 2. Reflexive Prop. 2. SUV STR 3. Corresponding Postulate 4. AD BA S 3. B SUV STR 4. AA Similarity S SV 5. VU A Reasons 1. RU bisects VU RT C D C T Proof: Proof: A P because of the definition of similar polygons. Since BD and QS are perpendicular to AC and PR, BDA QSP. So, AC Prove: DA SR RT S Q B SRT. 5. Def. of SR RT 6. URT VUR 6. Alternate Interior Theorem 7. VRU URT 7. Def. of 8. VUR VRU 8. Transitive Prop. BDA Given ADB A s ACD AA Similarity A Reflexive Prop. AC — DA AD — BA Def. of polygons bisector 9. If 2 of a are , the sides opp. these are . 9. VU VR 10. VU VR 10. Def. of S 11. VV R SR RT 11. Substitution 35. Given: JF bisects EFG. EH FG, EF HG Prove: EK KF GJ JF J E K H F Proof: RST ABC, W and D are midpoints of TS and CB, respectively. Prove: RWS ADB 37. Given: G A Statements Reasons R 1. JF bisects EFG. EH FG, EF HG 1. Given 2. EFK KFG 3. KFG JKH 4. 5. JKH EFK EKF EKF 6. FJH EFK 7. 8. FJH EKF EKF GJF 2. Def. of bisector 3. Corresponding Postulate 4. Vertical are . 5. Transitive Prop. 6. Alternate Interior Theorem 7. Transitive Prop. 8. AA Similarity 9. EK KF GJ JF 9. Def. of B S D C T W Proof: RST ABC Given RS — AB s RS — AB RS — AB polygons 2WS — 2BD WS — BD Def. of Division 178 B polygons W and D are midpoints. TS — CB Def. of S Def. of Substitution Chapter 6 segments Given 2WS TS 2BD CB Def. of midpoint RWS ADB SAS Similarity ...
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