Chapter 12.7, Problem 18PPS

To determine

Write whether the given Euclidean statement have some corresponding statement in spherical geometry.

Answer to Problem 18PPS

Yes, If point M is the midpoint of spherical segment AM, then spherical segment AM is congruent to spherical segment MB.

Explanation of Solution

Given:

It is given in the question that the statement is “If M is the midpoint of $\overline{AB}$ , then $\overline{AB}\cong \overline{MB}$ ”.

Here, The statement is similar in spherical geometry. So, the statement If M is the midpoint of $\overline{AB}$ , then $\overline{AB}\cong \overline{MB}$ ” may be written like that If point M is the midpoint of spherical segment AM, then spherical segment AM is congruent to spherical segment MB.