# Lesson 4

Dilating Lines and Angles

### Problem 1

Angle $$ABC$$ is taken by a dilation with center $$P$$ and scale factor 3 to angle $$A’B’C’$$. The measure of angle $$ABC$$ is $$21^\circ$$. What is the measure of angle $$A’B’C’$$?

### Solution

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### Problem 2

Select all lines that could be the image of line $$m$$ by a dilation.

A:

$$\ell$$

B:

$$m$$

C:

$$n$$

D:

$$o$$

E:

$$p$$

### Solution

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### Problem 3

Dilate line $$f$$ with a scale factor of 2. The image is line $$g$$. Which labeled point could be the center of this dilation?

A:

$$A$$

B:

$$B$$

C:

$$C$$

D:

$$D$$

### Solution

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### Problem 4

Quadrilateral $$A’B’C’E’$$ is the image of quadrilateral $$ABCE$$ after a dilation centered at $$F$$. What is the scale factor of this dilation?

### Solution

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(From Unit 3, Lesson 3.)

### Problem 5

A polygon has a perimeter of 18 units. It is dilated with a scale factor of $$\frac32$$. What is the perimeter of its image?

A:

12 units

B:

24 units

C:

27 units

D:

30 units

### Solution

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(From Unit 3, Lesson 3.)

### Problem 6

Solve the equation.

$$\frac{4}{7}=\frac{10}{x}$$

### Solution

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(From Unit 3, Lesson 1.)

### Problem 7

Here are some measurements for triangle $$ABC$$ and triangle $$XYZ$$:

• Angle $$CAB$$ and angle $$ZXY$$ are both 30 degrees
• $$AC$$ and $$XZ$$ both measure 3 units
• $$CB$$ and $$ZY$$ both measure 2 units

Andre thinks thinks these triangles must be congruent. Clare says she knows they might not be congruent. Construct 2 triangles with the given measurements that aren't congruent. Explain why triangles with 3 congruent parts aren't necessarily congruent.

### Solution

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(From Unit 2, Lesson 11.)