+327 1.Kayla wants to find the width, AB, of a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 22 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 and are similar? Why or why not?
(b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain.
***My Answers***
(a) No, because ABC and EDC are right triangles but have different length of bases.
(b) 145.45 ft
22/100=32/x =145.45
+9491 (a)
Remember, similar triangles can have different side lengths.
In order for two triangles to be similar, the angles must be the same.
Since ∠DCE and ∠BCA are vertical angles, they have the same measure.
Since ∠CDE and ∠CBA are right angles, they have the same measure.
And since two of the angles are the same, the third angle must be the same,
so △ABC is similar to △EDC by the Angle-Angle similarity rule.
(b)
To solve this, we have to know that △ABC is similar to △EDC .
Because △ABC is similar to △EDC , we can say that
22/100 = 32/x , where x is the length of AB in feet.
x = 3200/22 ≈ 145.45
So the width of the river is about 145.45 feet, just as you found! 
+9491 (a)
Remember, similar triangles can have different side lengths.
In order for two triangles to be similar, the angles must be the same.
Since ∠DCE and ∠BCA are vertical angles, they have the same measure.
Since ∠CDE and ∠CBA are right angles, they have the same measure.
And since two of the angles are the same, the third angle must be the same,
so △ABC is similar to △EDC by the Angle-Angle similarity rule.
(b)
To solve this, we have to know that △ABC is similar to △EDC .
Because △ABC is similar to △EDC , we can say that
22/100 = 32/x , where x is the length of AB in feet.
x = 3200/22 ≈ 145.45
So the width of the river is about 145.45 feet, just as you found!
