Chapter 2.4, Problem 5CYP

To determine

To find: The valid conclusion from the given statements, if possible. Then state whether the conclusion was drawn using the Law of Detachment or the Law of Syllogism.

Answer to Problem 5CYP

The valid conclusion is given above.

Explanation of Solution

Given:

The given statements are as given below.

The mid-point divides segments into two congruent segments.

If two segments are congruent, then their measures are equal.

  $M$ is the mid-point of $\overline{AB}$ .

Rewrite the given statements as below:

(1): If a mid-point divides a line segments then two segments are congruent.

(2): If two segments are congruent, then their measures are equal.

Let $p,q,r$ represent the parts of the given statements.

  $p$ : Mid-point divides a line segments.

  $q$ : Two segments are congruent.

  $r$ : Their measures are equal.

Since $M$ is the mid-point of $\overline{AB}$ satisfies the hypothesis $p$ is true. By using the Law of Syllogism , a valid conclusion is: The measure of $\overline{AM}\&\overline{MB}$ are equal.

Therefore, the valid conclusion is given above.