SOLUTION: Help please 1. Which of the following shows that ΔPQS ≅ ΔRQS, when x = 6? Graph :http://my.thinkwell.com/questionbank/95001-96000/95595/img/238168.jpg O

Algebra ->  Graphs -> SOLUTION: Help please 1. Which of the following shows that ΔPQS ≅ ΔRQS, when x = 6? Graph :http://my.thinkwell.com/questionbank/95001-96000/95595/img/238168.jpg O      Log On


   

Question 947706: Help please

1. Which of the following shows that ΔPQS ≅ ΔRQS, when x = 6?
Graph :http://my.thinkwell.com/questionbank/95001-96000/95595/img/238168.jpg
Options:
A. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242273.gif
B. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242274.gif
C. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242275.gif
D. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242276.gif
2. Which of the following uses the given set of points to prove that ΔABC≅ ΔEFD?
A(0, 0), B(3, 0), C(2, 3),
D(3, 0), E(1, 3), F(4, 3)
Options:
A. http://my.thinkwell.com/questionbank/95001-96000/95614/img/242277.gif
B. http://my.thinkwell.com/questionbank/95001-96000/95614/img/242278.gif
C. http://my.thinkwell.com/questionbank/95001-96000/95614/img/242279.gif
D.http://my.thinkwell.com/questionbank/95001-96000/95614/img/242280.gif
3. Given that PS is the perpendicular bisector of QR, PQ=12.4. and SR=7.6, identify QR.
Graph: http://my.thinkwell.com/questionbank/95001-96000/95629/img/238204.jpg
Options:
QR = 24.8
QR = 15.2
QR = 12.4
QR = 7.6
4. Identify the correct justification for each step, given that m ∠1 = 40° and m∠2 = 40°.
Diagram: http://my.thinkwell.com/questionbank/97001-98000/97606/img/238061.jpg
1. m∠1 = 40°, m∠2 = 40°
2. m∠1 + m∠3 = m∠ABD
3. ∠2 and ∠ABD are supplementary
4. m∠2 + m∠ABD = 180°
5. m∠2 + m∠1 + m∠3 = 180°
6. 40° + 40° + m∠3 = 180°
7. 80° + m∠3 = 180°
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
B. http://my.thinkwell.com/questionbank/95001-96000/95595/img/242274.gif
< PQS ≅ RQS
SQ ≅ SQ
PQ ≅ RQ true because if x=6 we have
PQ=3x%2B1=3%2A6%2B1=18%2B1=19
RQ=2x%2B7=2%2A6%2B7=12%2B7=19
so, < PQS ≅ < RQS by SAS

2.
B. http://my.thinkwell.com/questionbank/95001-96000/95614/img/242278.gif
check distances:
A(0, 0), B(3, 0),
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%283-0%29%5E2+%2B+%280-0%29%5E2%29=+3+


For more on this concept, refer to Distance formula.


AB=3
E(1, 3), F(4, 3)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%284-1%29%5E2+%2B+%283-3%29%5E2%29=+3+


For more on this concept, refer to Distance formula.


EF=3
B(3, 0), C(2, 3),
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%282-3%29%5E2+%2B+%283-0%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.


we can write it as d=sqrt%28%28-1%29%5E2%2B3%5E2%29=sqrt%2810%29
BC=sqrt%2810%29
F(4, 3) ,D(3, 0)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%283-4%29%5E2+%2B+%280-3%29%5E2%29=+3.16227766016838+


For more on this concept, refer to Distance formula.


FD=sqrt%2810%29

C(2, 3), A(0, 0)
D(3, 0),E(1, 3)
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%280-2%29%5E2+%2B+%280-3%29%5E2%29=+3.60555127546399+


For more on this concept, refer to Distance formula.


d=sqrt%282%5E2%2B3%5E2%29=sqrt%2813%29
CA=sqrt%2813%29
Solved by pluggable solver: Distance Formula to determine length on coordinate plane
The distance (d) between two points is given by the following formula:

d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%281-3%29%5E2+%2B+%283-0%29%5E2%29=+3.60555127546399+


For more on this concept, refer to Distance formula.


d=sqrt%28%28-2%29%5E2%2B3%5E2%29=sqrt%2813%29
DE=sqrt%2813%29
this proves that Δ ABC ≅ Δ 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%2BSQ since PS is the perpendicular bisector of QR we can conclude that SR=SQ+ and plug in SR=7.6
QR=7.6%2B7.6
QR=15.2

4.
Identify the correct justification for each step, given that m ∠ 1+=+40° and m ∠ 2+=+40°.
1. m∠1 = 40°, m∠2 = 40°.........given
2. m∠1 + m∠3 = m∠ABD..........Angle Addition Postulate;;
3. ∠2 and ∠ABD are supplementary..............Vertical angles theorem
4. m∠2 + m∠ABD = 180°...............Def. of Supplementary angles
5. m∠2 + m∠1 + m∠3 = 180°..........Angle Addition Postulate;
6. 40° + 40° + m∠3 = 180°............Substitution property of =
7. 80° + m∠3 = 180° ..................Simplify