Lesson 4

Dilating Lines and Angles

  • Let’s dilate 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 \(A’B’C’\)?

Problem 2

Select all lines that could be the image of line \(m\) by a dilation.

Lines o, l, m, n, and p. Line o intersects all lines, runs downward and to the right. Line L intersects lines o, m and n. Lines m, n and p are parallel to each other.  
A:

\(\ell\)

B:

\(m\)

C:

\(n\)

D:

\(o\)

E:

\(p\)

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?

Line f and g with given points.
A:

\(A\)

B:

\(B\)

C:

\(C\)

D:

\(D\)

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?

Quadrilaterals A B C E and A prime B prime C prime E prime.
(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

(From Unit 3, Lesson 3.)

Problem 6

Solve the equation. 

\(\frac{4}{7}=\frac{10}{x}\)

(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.

(From Unit 2, Lesson 11.)