# Splitting Triangle Sides with Dilation, Part 1

# Splitting Triangle Sides with Dilation, Part 1

##### Problem 1

1) What is the measure of angle $A'B'C$?

##### Problem 2

2) Triangle $DEF$ is formed by connecting the midpoints of the sides of triangle $ABC$. The lengths of the sides of $DEF$ are shown. What is the length of $AB$?

##### Problem 3

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

##### Problem 4

4) Draw 2 lines that could be the image of line $m$ by a dilation. Label the lines $n$ and $p$.

##### Problem 5

5) Is it possible for polygon $ABCDE$ to be dilated to figure $VWXYZ$?

6) Explain your reasoning.

##### Problem 6

7) Triangle $XYZ$ is scaled and the image is $X'Y'Z'$. Select **all** of the equations that could be used to solve for $a$. Write each corresponding letter in the answer box and separate letters with commas.

a) $\frac{8}{5} = \frac{3}{a}$ $\quad\quad$ b) $\frac{5}{8} = \frac{3}{a}$ $\quad\quad$ c) $\frac{8}{3} = \frac{5}{a}$ $\quad\quad$ d) $\frac{3}{8} = \frac{5}{a}$ $\quad\quad$ e) $\frac{8}{a} = \frac{5}{3}$

##### Problem 7

8) Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that $EFGH$ is a parallelogram and angle $HEF$ is a right angle, write a statement that will help prove angle $FGH$ is also a right angle.

9) Han then states that the 2 triangles created by diagonal $EG$ must be congruent. Help Han write a proof that triangle $EHG$ is congruent to triangle $GFE$.