CPCTC. The Bigger Picture.

Note: In this post we will not try to explain the process of proofs. The underlying assumption is that the reader has a basic Geometry understanding of proofs, triangle congruence, and the results of parallel lines cut by a transversal...

CPCTC is an acronym used in Geometry that means: "Corresponding Parts of Congruent Triangles are Congruent."

For example, consider the geometric proof...

Students who have been trained in the dialectical phase of their eduction, will find proofs a challenge rather than a burden.

The proof here will run something like this.

In the proof, step 6, we use CPCTC in order to justify the congruence relation between angle EDG and angle FGD.

But what is CPCTC and is there anyway under the sun to Biblically integrate this lesson?

Look at step 5 again. In this step we declare the triangles to be congruent. Therefore the parts of the triangles must also be congruent. That is what CPCTC is all about In other-words, understanding the truth about the bigger picture (the triangles are congruent) leads to a truth of the smaller picture (the corresponding sides and angles must also be congruent.) We move from the general to the specific.

The Biblical Integration

If we think about what CPCTC means, it all boils down to "individual truth resulting from a larger truth." In other words, the natural outcome (or result) of triangle congruence is that their parts are also congruent. CPCTC follows, therefore, from the definition of triangle congruence.

We will use this to look at scripture and think of ways that knowing God and His character can lead to other results. Let us first get our students thinking by asking pointed questions that make them think about God's reaching out to humanity as a whole, and then to the beautiful consequences of what it means to them personally.

Questions:

1. What does it mean that 'God so loved the world...'? John 3:16

2. Does this have any implications to you individually?

3. What does it mean that 'all have sinned...'? Romans 3:23

4. Does this have any implications to you individually?

5. What does it mean that 'if anyone confesses their sins, then God will forgive their sins...' 1 John 1:9

6. Does this have any implications to you individually?

"You see class, each question I asked you went from the general to the specific. Because God loved the world, he also loves you. Because all have sinned, this means that you and I have sinned. Because God forgives those who confess their sins, means that God will forgive you and I when we confess our sins. Each time we move from the general to the specific.

Likewise, in a pair of triangles, If we know that both triangles are congruent, then we may also conclude that the individual (specific) parts are also congruent. The truth of the whole, leads to the same truth applying the corresponding individual components."

John Partridge

December 20th 2018