Use the Law of Syllogism to determine whether a valid...

Name: Problem 4, Chapter 2: Geometry
Uploaded: 2020-10-26T18:00:10-08:00
Duration: 3 min 52 s
Channel: Nathaniel Plew
Description: Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements. If a valid conclusion is possible, write it. If not, write no conclusion. The midpoint divides a segment into two congruent segments. If two segments are congruent, then their measures are equal.

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements. If a valid conclusion is possible, write it. If not, write no conclusion. The midpoint divides a segment into two congruent segments. If two segments are congruent, then their measures are equal.

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements. If a valid conclusion is possible, write it. If not, write no conclusion.
The midpoint divides a segment into two congruent segments. If two segments are congruent, then their measures are equal.

Key Concepts

Law of Syllogism

The law of syllogism is a logical rule that allows one to combine conditional statements. It states that if one statement implies a second, and the second implies a third, then the first statement implies the third. This principle is essential in constructing direct logical inferences and conclusions.

Segment Congruence

Segment congruence in geometry refers to segments that have the same length. When two segments are congruent, they are equal in measure, which provides a basis for making further comparisons or drawing conclusions about geometric properties.

Midpoint in Geometry

The midpoint of a segment is the point that divides the segment into two equal parts. By definition, the two resulting segments are congruent, meaning they have equal measure. This concept is key in proofs and problems involving bisected lines and symmetry in geometric figures.

Transcript

00:01 So for number four, we're told to use the law of syllogism to determine whether or not a valid conclusion can be reached, given the statements that it gives you in the question.

00:13 So if you can, then we write what the conclusion we reached was, and if we can't, then we write no conclusion.

00:20 So for number four, our statements are, if a midpoint divides a segment in the two congruent segments.

00:26 Our statements are firstly that the midpoint divides a segment into two congruent segments.

00:33 Next, we know if two congruent segments are congruent, then their measures are equal.

00:41 So the law of syllogism, if we remember, states that if conditional, if conditional pq is true, and conditional, we can write this out in the actual notation.

00:56 So if conditional if conditional pq is true and conditional qr is true, then that would mean that conditional pr is also true.

01:17 So all this fancy notation is just how you write out conditionals.

01:21 So we have our brackets here, which is our, essentially our big conditional, because this whole thing is a conditional on its own.

01:29 So we're assuming if everything in this thing is true and this is true, then this is true.

01:36 Those are these arrows mean.

01:38 So we're assuming if this is true, like if this relationship is a true thing and this symbol here means and this relation right here is true, then this whole thing is true.

01:50 And then if this is true, then we know this must be true, according to the law of syllogism.

01:57 So we'll let this out an example...

Please give Ace some feedback