# Lesson 5

Splitting Triangle Sides with Dilation, Part 1

- Let’s draw segments connecting midpoints of the sides of triangles.

### Problem 1

What is the measure of angle \(A’B’C\)?

\(20^\circ\)

\(40^\circ\)

\(60^\circ\)

\(80^\circ\)

### Problem 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

Angle \(ABC\) is taken by a dilation with center \(P\) and scale factor \(\frac13\) to angle \(A’B’C’\). The measure of angle \(ABC\) is \(21^\circ\). What is the measure of angle \(A’B’C’\)?

### Problem 4

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

### Problem 5

Is it possible for polygon \(ABCDE\) to be dilated to figure \(VWXYZ\)? Explain your reasoning.

### Problem 6

Triangle \(XYZ\) is scaled and the image is \(X'Y'Z'\). Write 2** **equations that could be used to solve for \(a\).

### Problem 7

- 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.
- 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 \(GFE\).