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

KennedyPape
Jan 23, 2018

#1**+3 **

(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!

hectictar
Jan 23, 2018

#1**+3 **

Best Answer

(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!

hectictar
Jan 23, 2018