Splitting Triangle Sides with Dilation, Part 1
- Let’s draw segments connecting midpoints of the sides of triangles.
What is the measure of angle \(A’B’C\)?
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 \(AB\)?
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 \(A’B’C’\)?
Draw 2 lines that could be the image of line \(m\) by a dilation. Label the lines \(n\) and \(p\).
Is it possible for polygon \(ABCDE\) to be dilated to figure \(VWXYZ\)? Explain your reasoning.
Triangle \(XYZ\) is scaled and the image is \(X'Y'Z'\). Write 2 equations that could be used to solve for \(a\).
- 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 \(GFE\).