We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Geometry Question: Triangle Similarity. Please Help!

+1
1721
1

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

Jan 23, 2018

### Best Answer

#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! Jan 23, 2018

### 1+0 Answers

#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