# Dilating Lines and Angles

ID: kuhuf-visat Illustrative Mathematics
Subject: Geometry

7 questions

# Dilating Lines and Angles

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##### 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) ﻿$\ell$﻿ b) ﻿$m$﻿ c) ﻿$n$﻿ d) ﻿$o$﻿ 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? a) $A$b) $B$c) $C$d) $D$
##### 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?

a) $\text{12 units}$b) $\text{24 units}$c) $\text{27 units}$d) $\text{30 units}$
##### Problem 6

6) Solve the equation.

﻿$\frac{4}{7} = \frac{10}{x}$﻿

##### Problem 7

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

• 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.