Question

Given: If two segments are congruent, then they have the

same measure. If two segments each have a measure of
6.5 centimeters, then they are congruent.
Conjecture: If two segments are congruent, then they
each have a measure of 6.5 centimeters.
Determine whether each conjecture is valid by the Law of Syllogism.

Answer 1

The conjecture that if two segments are congruent, then they each have a measure of 6.5 centimeters is valid by the Law of Syllogism.

Step-by-step explanation:

The conjecture If two segments are congruent, then they each have a measure of 6.5 centimeters is valid by the Law of Syllogism. The Law of Syllogism states that if p implies q, and q implies r, then p implies r. In this case, we are given that if two segments are congruent, then they have the same measure (p implies q), and if two segments each have a measure of 6.5 centimeters, then they are congruent (q implies r). Therefore, we can conclude that if two segments are congruent, then they each have a measure of 6.5 centimeters (p implies r).