# Splitting Triangle Sides with Dilation, Part 1

ID: damik-dasih
Illustrative Mathematics
Subject: Geometry

9 questions

# Splitting Triangle Sides with Dilation, Part 1

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##### Problem 1

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

a) $20 \degree$b) $40 \degree$c) $60 \degree$d) $80 \degree$
##### 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 ﻿$VWXYZ$﻿?

True or false? Write below.

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) ﻿$\frac{8}{a} = \frac{5}{3}$﻿
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 ﻿$GFE$﻿.