Exercise 35 Page 349

In order to determine the relationship between $R P$ and $M P,$ we can use Theorem $5.10$ about Angle-Side Relationships in Triangles.

Angle-Side Relationships in Triangles
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Note that this theorem is used to compare the sides of a triangle. Therefore, because

\overline{R P}

and

\overline{M P}

are two sides of

△ M R P,

we will consider the interior angles of

△ M R P .

Keeping this information in mind, let's consider the given diagram.