Question

evaluate independent practice
lesson 12.3 homework
complete problems 1-6 below for independent practice.
when you are finished, check the solutions with your teacher.

1. if \\(\delta fgh \sim \delta tsr\\), find the value of \\(gh\\).
2. if \\(\delta fgh \sim \delta tuh\\), find the value of \\(ht\\).
3. if \\(\delta wvt \sim \delta rst\\), find the value of \\(vt\\).
4. \\(\delta klm \sim \delta kcd\\) are similar. solve for \\(x\\).
5. \\(\delta efg \sim \delta ekl\\) are similar. solve for \\(x\\).
6. \\(\delta klm \sim \delta kqp\\) are similar. solve for \\(x\\).

Explanation:

Set up similarity ratios for Question 1

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta FGH \sim \Delta TSR\).
The ratio of corresponding sides is:

$$\frac{GH}{SR} = \frac{FG}{TS}$$

Substitute the given values \(FG = 104\), \(TS = 39\), and \(SR = 30\):

$$\frac{GH}{30} = \frac{104}{39}$$

Using the Solving Linear Equations knowledge point:

$$GH = 30 \cdot \frac{104}{39} = 30 \cdot \frac{8}{3} = 80$$

Set up similarity ratios for Question 2

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta FGH \sim \Delta TUH\).
The ratio of corresponding sides is:

$$\frac{HT}{HF} = \frac{TU}{FG}$$

Substitute the given values \(HF = 84\), \(TU = 45\), and \(FG = 108\):

$$\frac{HT}{84} = \frac{45}{108}$$

Using the Solving Linear Equations knowledge point:

$$HT = 84 \cdot \frac{45}{108} = 84 \cdot \frac{5}{12} = 35$$

Set up similarity ratios for Question 3

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta WVT \sim \Delta RST\).
The ratio of corresponding sides is:

$$\frac{VT}{ST} = \frac{WT}{RT}$$

Substitute the given values \(ST = 104\), \(WT = 66\), and \(RT = 143\):

$$\frac{VT}{104} = \frac{66}{143}$$

Using the Solving Linear Equations knowledge point:

$$VT = 104 \cdot \frac{6}{13} = 8 \cdot 6 = 48$$

Set up similarity ratios for Question 4

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta KLM \sim \Delta KCD\).
The ratio of corresponding sides is:

$$\frac{KC}{KL} = \frac{CD}{LM}$$

Substitute the given values \(KC = 2x - 8\), \(KL = 63\), \(CD = 16\), and \(LM = 28\):

$$\frac{2x - 8}{63} = \frac{16}{28}$$

Using the Solving Linear Equations knowledge point:

$$\frac{2x - 8}{63} = \frac{4}{7}$$

$$2x - 8 = 63 \cdot \frac{4}{7} = 36$$

$$2x = 44 \implies x = 22$$

Set up similarity ratios for Question 5

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta EFG \sim \Delta EKL\).
The ratio of corresponding sides is:

$$\frac{EG}{EL} = \frac{EF}{EK}$$

Substitute the given values \(EG = 3x + 20\), \(EL = 14\), \(EF = 32\), and \(EK = 8\):

$$\frac{3x + 20}{14} = \frac{32}{8}$$

Using the Solving Linear Equations knowledge point:

$$\frac{3x + 20}{14} = 4$$

$$3x + 20 = 56$$

$$3x = 36 \implies x = 12$$

Set up similarity ratios for Question 6

Using the Similarity Statements and Corresponding Sides of Similar Figures knowledge points:
Given \(\Delta KLM \sim \Delta KQP\).
The ratio of corresponding sides is:

$$\frac{KL}{KQ} = \frac{KM}{KP}$$

Substitute the given values \(KL = 3x - 1\), \(KQ = 7\), \(KM = 8\), and \(KP = 4\):

$$\frac{3x - 1}{7} = \frac{8}{4}$$

Using the Solving Linear Equations knowledge point:

$$\frac{3x - 1}{7} = 2$$

$$3x - 1 = 14$$

$$3x = 15 \implies x = 5$$

Answer:

No.	Answer
2	\(HT = 35\)
3	\(VT = 48\)
4	\(x = 22\)
5	\(x = 12\)
6	\(x = 5\)