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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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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus

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