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Pre-Calculus Homework Solutions 163

Pre-Calculus Homework Solutions 163 - Substitute the known...

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Unformatted text preview: Substitute the known values and let x be the height of the pyramid. 35. Given: LP MN LJ Prove: JN Proof: 114)(3) ¬ (125 3(3) 717 ¬9 9x ¬6(717) 9x ¬4302 x ¬478 The pyramid was about 478 feet tall at that time. x 2(3) x 6 Prove: Q 1. QP 2. AB EF; DE APQ AQP 3. AQP E 4. ABC AQP AB 5. AQ BC QP 6. AB QP AB EF 7. QP 1. Given NMJ 3. AA Similarity PJ JM b. Prove: BC BE 3. Transitive Prop. of 4. AA Similarity 37. Given: E J D BD BA BAC and AB DE s Prove: 6. Cross products EDF are right triangles. AC DF ABC B DEF E 7. Def. of segments EF 4. Corr. sides of s are proportional. Proof: From part a, A CDB by definition of similar triangles. ABE DBC because all right angles are congruent. Thus, ABE DBC by AA Similarity. BC BD BE BA from definition of similar triangles. 2. Corresponding Postulate 5. Def. of AQ BC DE BC LPJ A B C Proof: AHB, AJC, and EBC are right angles because perpendicular lines form right angles. Since all right angles are congruent, AHB AJC EBC. Since A A by the Reflexive Property, ABH ACJ, by AA Similarity. Likewise, since C C, ACJ DCB. By the Transitive Property, ABH DCB. BC EF B 2. Alternate Interior Theorem H Reasons C LNM, PMN 36. Given: EB AC, BH AE, CJ AE a. Prove: ABH DCB F E, QP BC; PLN LPM LJ 4. JN P B 1. Given 3. D B CE Proof: Statements Reasons 2. DEF A N 1. LP MN BC EF ABC P J M Statements 33. x must equal y. If BD AE, then CBD CAE because they are corresponding angles and C C so BCD ACE by AA Similarity. DC x Then BC . Thus, 2 x y . Cross multiply AC EC 4 and solve for y. 2 x 4 ¬x y 2(x y) ¬4x 2x 2y ¬4x 2y ¬2x y ¬x 34. Given: B E; QP BC; QP EF; AB DE L PJ JM A Proof: Statements 8. AB EF AQ BC 8. Substitution 9. AQ BC DE BC 9. Substitution CD F Reasons 1. BAC and EDF are right triangles. 1. Given BAC and EDF are right angles. 2. Def. of rt. 10. AQ DE 10. Div. Prop. 2. 11. AQ DE 11. Def. of segments 3. 12. SAS AB 4. DE 13. CPCTC 5. 12. AQP 13. APQ 14. C 15. ABC DEF F BAC ABC EDF AC DF 3. All rt. are . 4. Given DEF 5. SAS Similarity 14. Transitive Prop. F DEF 15. AA Similarity 165 Chapter 6 ...
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