Question 947706
1. 

B. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242274.gif

< {{{PQS}}} &#8773;  {{{RQS}}}
{{{SQ}}} &#8773; {{{SQ}}}
{{{PQ}}} &#8773; {{{RQ}}} true because if {{{x=6}}} we have

{{{PQ=3x+1=3*6+1=18+1=19}}}
{{{RQ=2x+7=2*6+7=12+7=19}}}

so, < {{{PQS}}} &#8773;  < {{{RQS}}} by {{{SAS}}}


2.

B. http://my.thinkwell.com/questionbank/95001-96000/95614/img/242278.gif

check distances:
A(0, 0), B(3, 0),

*[invoke Distance_Formula_for_Coordinate_Plane 0, 0, 3, 0]

{{{AB=3}}}

 E(1, 3), F(4, 3) 

*[invoke Distance_Formula_for_Coordinate_Plane 1, 3, 4, 3]

{{{EF=3}}}

B(3, 0), C(2, 3),
*[invoke Distance_Formula_for_Coordinate_Plane 3, 0, 2, 3]

we can write it as {{{d=sqrt((-1)^2+3^2)=sqrt(10)}}}

{{{BC=sqrt(10)}}}

F(4, 3) ,D(3, 0)

*[invoke Distance_Formula_for_Coordinate_Plane 4, 3, 3, 0]

{{{FD=sqrt(10)}}}


C(2, 3), A(0, 0)
D(3, 0),E(1, 3)

*[invoke Distance_Formula_for_Coordinate_Plane 2, 3, 0, 0]

{{{d=sqrt(2^2+3^2)=sqrt(13)}}}
{{{CA=sqrt(13)}}}

*[invoke Distance_Formula_for_Coordinate_Plane 3, 0, 1, 3]

{{{d=sqrt((-2)^2+3^2)=sqrt(13)}}}

{{{DE=sqrt(13)}}}

this proves that &#916; {{{ABC}}} &#8773; &#916; {{{EFD}}} by {{{SSS}}}



3.Given that {{{PS}}} is the perpendicular {{{bisector}}} of {{{QR}}}, {{{PQ=12.4}}}. and {{{SR=7.6}}}, identify {{{QR}}}. 

answer:{{{QR=15.2}}}

proof:

{{{QR=SR+SQ}}}  since {{{PS}}} is the perpendicular {{{bisector}}} of {{{QR}}} we can conclude that {{{SR=SQ }}} and plug in {{{SR=7.6}}}

{{{QR=7.6+7.6}}}

{{{QR=15.2}}}


4.
Identify the correct justification for each step, given that {{{m}}} &#8736; {{{1 = 40}}}° and {{{m}}} &#8736; {{{2 = 40}}}°. 

 1. m&#8736;1 = 40°, m&#8736;2 = 40°.........given
2. m&#8736;1 + m&#8736;3 = m&#8736;ABD..........Angle Addition Postulate;; 
3. &#8736;2 and &#8736;ABD are supplementary..............Vertical angles theorem
4. m&#8736;2 + m&#8736;ABD = 180°...............Def. of Supplementary angles 
5. m&#8736;2 + m&#8736;1 + m&#8736;3 = 180°..........Angle Addition Postulate;
6. 40° + 40° + m&#8736;3 = 180°............Substitution property of = 
7. 80° + m&#8736;3 = 180° ..................Simplify