Chapter 7, Problem 9ASNE

To determine

To fill: the blank in the given statement with the correct word among always, sometimes or never.

Answer to Problem 9ASNE

Sometimes(S)

Explanation of Solution

Given information:

The given statement is “If $\overline{RS}\cong \overline{MN,}$ $\overline{ST}\cong \overline{NO,}$ and $\angle R\cong \angle M$ then $\Delta RST$ and $\Delta MNO$ are $\underset{\_}{}$ congruent”.

Consider the triangles below,

  

The triangles $\Delta RST$ and $\Delta MNO$ are having two corresponding sides and one non

included angle which are congruent. But there is no Side-Side- angle or Angle −Side-Side

postulate. Thus the triangles are not necessarily congruent.

Therefore, the triangles are sometimes congruent.

Hence, the correct word is Sometimes(S).