# Dilating Lines and Angles

# Dilating Lines and Angles

##### Problem 1

1) Angle $ABC$ is taken by dilation with center $P$ and scale factor 3 to angle $A'B'C'$. The measure of angle $ABC$ is $21\degree$. What is the measure of angle $A'B'C'$?

##### Problem 2

2) Select **all** lines that could be the image of line $m$ by a dilation. Write each corresponding letter in the answer box and separate letters with commas.

a) $l$ $\quad\quad$ b) $m$ $\quad\quad$ c) $n$ $\quad\quad$ d) $o$ $\quad\quad$ e) $p$

##### Problem 3

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?

##### Problem 4

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?

##### Problem 5

5) A polygon has a perimeter of 18 units. It is dilated with a scale factor of $\frac{3}{2}$. What is the perimeter of its image?

##### Problem 6

6) Solve the equation.

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

##### Problem 7

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

$\bullet \ \$ Angle $CAB$ and angle $ZXY$ are both 30 degrees

$\bullet \ \ AC$ and $XZ$ both measure 3 units

$\bullet \ \ CB$ 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.