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?

KindaFrisky Mar 30, 2021

#1**+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

CPhill Mar 30, 2021

#2**+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

CPhill Mar 30, 2021

#3**+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°

CPhill Mar 30, 2021

#4**+1 **

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

KindaFrisky
Mar 30, 2021

#5**+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

civonamzuk Mar 31, 2021