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
(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!
(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!