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1. Three segments have a total length of 26 inches. The first segment is two less than three times the second segment. The third segment is one more than five times the second segment. What are the lengths of the three segments? 

All three variables must be defined in terms of x.

 

2. A triangle with sides 8m, 11m and an included angle of 45°.  

How many triangles can be produced: _______

Explain:

 

3. A triangle with angles 

25°, 56°, and 99°

How many triangles can be produced: _______

Explain:

 

4.The ratio of similar triangles △ACB to △DFE is 2/5 and  AB = 8.  What is the length of DE? 

 

5. △ACB is similar to △DFE.  The m ∠ABC = 35 and the m∠ACB = 80. What is the measure of ∠FDE?

 Mar 30, 2021
 #1
avatar+118470 
+2

1. Three segments have a total length of 26 inches. The first segment is two less than three times the second segment. The third segment is one more than five times the second segment. What are the lengths of the three segments? 

All three variables must be defined in terms of x.

 

 

(3x - 2)  +  x  +  ( 5x + 1)  =  26

 

9x - 1  = 26

 

9x  =  26 + 1

 

9x  =  27

 

x = 27 / 9  =  3

 

First segment  =   3(3) - 2   =   7  in

Second segment =  3  in

Third segment  =  5(3) + 1   =  16 in

 

cool cool cool

 Mar 30, 2021
 #2
avatar+118470 
+2

2. A triangle with sides 8m, 11m and an included angle of 45°.  

How many triangles can be produced: _______

Explain:

 

One triangle.....we  have a SAS  situation.......the triangle  is well-defined

 

3. A triangle with angles 

25°, 56°, and 99°

How many triangles can be produced: _______

Explain:

 

An infinite  number  of similar triangles could  be  produced

 

cool cool cool

 Mar 30, 2021
 #3
avatar+118470 
+2

4.The ratio of similar triangles △ACB to △DFE is 2/5 and  AB = 8.  What is the length of DE? 

 

DE / AB =  5/2

 

So

 

DE  =  (5/2)AB

 

DE  = (5/2) * 8   =   20

 

5. △ACB is similar to △DFE.  The m ∠ABC = 35 and the m∠ACB = 80. What is the measure of ∠FDE?

 

FDE  =  CAB   =  180 - mABC -m ACB =    180  - 35  - 80  =  180  - 115   =  65°

 

 

cool cool cool

 Mar 30, 2021
 #4
avatar+58 
+1

thank you so much! I don't know how I would've gotten through without you! :D

KindaFrisky  Mar 30, 2021
 #5
avatar+1203 
+3

1. Three segments have a total length of 26 inches. The first segment is 2 less than three times the second segment. The third segment is 1 more than five times the second segment. What are the lengths of the three segments? 

All three variables must be defined in terms of x.

 

1st      3x - 2

2nd     x

3rd      5x + 1

 

3x - 2 + x + 5x + 1 = 26

9x = 27

x = 3

 Mar 31, 2021

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