# 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.

\(\ell\)

\(m\)

\(n\)

\(o\)

\(p\)

### 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?

\(A\)

\(B\)

\(C\)

\(D\)

### 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?

12 units

24 units

27 units

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.)