SOLUTION: Given that A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0), and F(0, 6), which of the following proves that ΔABC ~ ΔDEF? A. http://my.thinkwell.com/questionbank/97001-980

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Question 954729: Given that A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0), and F(0, 6), which of the following proves that ΔABC ~ ΔDEF?
A. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244855.gif
B. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244856.gif
C. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244844.gif
D. ΔABC and ΔDEF are not similar.
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

AB/DE=4/12=1/3
CA/FD=2/6=1/3
The triangles are similar.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

first find out what is the distance between given points A(, ), B(, ), C(, )(vertices of a triangle )
and the distance between given points D(, ), E(, ), and F(, ) (vertices of a triangle )
these distances are the lengths of the sides
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (0, 0), we can say (x1, y1) = (0, 0)
So ,


Since the second point is (4, 0), we can also say (x2, y2) = (4, 0)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (0, 0) and (4, 0)






Plug in , , , and













==========================================================

Answer:


The distance between the two points (0, 0) and (4, 0) is exactly 4 units




Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (0, 0), we can say (x1, y1) = (0, 0)
So ,


Since the second point is (0, 2), we can also say (x2, y2) = (0, 2)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (0, 0) and (0, 2)






Plug in , , , and













==========================================================

Answer:


The distance between the two points (0, 0) and (0, 2) is exactly 2 units




Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (4, 0), we can say (x1, y1) = (4, 0)
So ,


Since the second point is (0, 2), we can also say (x2, y2) = (0, 2)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (4, 0) and (0, 2)






Plug in , , , and






















==========================================================

Answer:


The distance between the two points (4, 0) and (0, 2) is exactly units


The approximate distance between the two points is about 4.47213595499958 units



So again,


Exact Distance: units


Approximate Distance: units




and
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (0, 0), we can say (x1, y1) = (0, 0)
So ,


Since the second point is (12, 0), we can also say (x2, y2) = (12, 0)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (0, 0) and (12, 0)






Plug in , , , and













==========================================================

Answer:


The distance between the two points (0, 0) and (12, 0) is exactly 12 units




Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (0, 0), we can say (x1, y1) = (0, 0)
So ,


Since the second point is (0, 6), we can also say (x2, y2) = (0, 6)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (0, 0) and (0, 6)






Plug in , , , and













==========================================================

Answer:


The distance between the two points (0, 0) and (0, 6) is exactly 6 units




Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (12, 0), we can say (x1, y1) = (12, 0)
So ,


Since the second point is (0, 6), we can also say (x2, y2) = (0, 6)
So ,


Put this all together to get: , , , and

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (12, 0) and (0, 6)






Plug in , , , and






















==========================================================

Answer:


The distance between the two points (12, 0) and (0, 6) is exactly units


The approximate distance between the two points is about 13.4164078649987 units



So again,


Exact Distance: units


Approximate Distance: units





A. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244855.gif







therefore
check:



so, the statement is true and therefore triangle ~ to triangle by
B. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244856.gif
this image shows that






which is not true for given points
so, this is an answer
C. http://my.thinkwell.com/questionbank/97001-98000/97647/img/244844.gif
this image shows that by the distance formula


and also


which is true, this is an answer either

so, your answer is:

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