91Ó°ÊÓ

If a line divides two sides of a triangle proportionally, then it is _________ to the third side. This theorem is known as the ___________.

COMPLETE THE SENTENCE two angles of one triangle are congruent to two angles of another triangle, then the triangles are ________

COMPLETE THE SENTENCE For two ? gures to be similar, the corresponding angles must be ____________, and the corresponding side lengths must be _________________

In \(\triangle \mathrm{ABC}\) , point \(\mathrm{R}\) lies on \(\overline{\mathrm{BC}}\) and \(\mathrm{AR}\) bisects \(\angle \mathrm{CAB}\) Write the proportionality statement for the triangle that is based on the Triangle Angle Bisector Theorem 8.9)

WRITING Can you assume that corresponding sides and corresponding angles of any two similar triangles are congruent? Explain.

In Exercises 7 and 8, verify that \(\triangle A B C \sim \Delta \mathrm{DEF}\) . Find the scale factor of \(\Delta \mathrm{ABC}\) to \(\Delta \mathrm{DEF}\). $$\Delta \mathrm{ABC} \cdot \mathrm{BC}=18, \mathrm{AB}=15, \mathrm{AC}=12$$ $$\Delta \mathrm{DEF} : \mathrm{EF}=12, \mathrm{DE}=10, \mathrm{DF}=8$$

In Exercises 7 and 8, verify that \(\triangle A B C \sim \Delta \mathrm{DEF}\) . Find the scale factor of \(\Delta \mathrm{ABC}\) to \(\Delta \mathrm{DEF}\). $$\Delta \mathrm{ABC} \cdot \mathrm{AB}=10, \mathrm{BC}=16, \mathrm{CA}=20$$ $$\Delta \mathrm{DEF} : \mathrm{DE}=25, \mathrm{EF}=40, \mathrm{FD}=50$$

Draw a segment with the given length. Construct the point that divides the segment in the given ratio. $$3 \mathrm{in} : 1 \text { to } 4$$

Draw a segment with the given length. Construct the point that divides the segment in the given ratio. $$2 \mathrm{in.} ; 2 \text { to } 3$$

Draw a segment with the given length. Construct the point that divides the segment in the given ratio. $$12 \mathrm{cm} ; 1 \text { to } 3$$