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Kayla wants to find the width, AB, of a river. She walks along the edge of the river 75 ft and marks point C. Then she walks 35 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.

(a) Can Kayla conclude that Δ𝐴𝐵𝐶 and Δ𝐸𝐷𝐶 are similar? 

 Why or why not? 

 (b) Suppose DE = 21 ft. What can Kayla conclude about the width of the river?

 Jan 29, 2020
 #1
avatar+21707 
+3

Yes they are similar triangles     angle   angle   angle        all three angles in each triangle are equal

 

Have you tried 'b' yet? ....similar triangles

 Jan 29, 2020
 #2
avatar+16 
+1

no, I haven't... D: 

 A is similar because of the AAA theorem?

upperclasspanda  Jan 29, 2020
 #3
avatar+21707 
+2

yes....

ElectricPavlov  Jan 29, 2020
 #4
avatar+16 
+1

could you help me with B please...and explain it to me..?

 Jan 29, 2020
 #5
avatar+21707 
+3

Since they are similar triangles, their sides are SIMILAR lengths....

One triangle has side length of   35    the other similar side in the OTHER triangle is 75 ft...

   you can make a ratio of the side lengths  35 is to  75     35/75   is the ratio of similar sides in the two triangles

       now they tell you DE is 21 feet.....and we are looking for the SIMILAR side in the other triangle, BA

          these two sides will be in the same ratio    35/75

             so you can say something like this   35 is to 75      as DE is to BA      and we know DE is 21, so this looks like this:

                                  35/75 = 21/BA          now solve for BA       ...   can you do that now?

ElectricPavlov  Jan 29, 2020
 #6
avatar+16 
0

no, well... I don't know for sure ... I get what you're saying but I can't solve BA because if its similar wouldn't BA be considered 75? . . . I'm sorry, I'm not math smart.. .

upperclasspanda  Jan 30, 2020
 #7
avatar+21707 
+2

'similar'   doesn't mean 'exactly the same' ....just kind of alike....in a ratio

the triangles are similar....so sides in triangle  edc   are similar to sides in triangle abc ....in a ratio......not exactly the same...they are 'alike'

 

      DC  is similar to  BC 

 

ED  is similar to AB                (and EC is similar to AC....but we do not need this for this question)

 

DC  is similar to  BC       as         ED  is similar to AB 

35   is similar to 75          as        21    is similar to AB

 

35/75  =  21/AB   

AB   =  21/ (35/75)

AB = 21 * 75/35                                  Look at things and think about it for a while....it becomes easier....and intuitive after a while  cheeky

ElectricPavlov  Jan 30, 2020

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