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.)