Unit 3 - 4
Key Objectives (from the notes):
- Use CPCTC to prove parts of triangles are congruent.
Lesson 4 is much more interesting. This time, we actually got introduced to something new!
The biggest thing that we took out of this lesson was this idea: corresponding parts of congruent triangles are congruent. I know, it's a mouthful; we just call it "CPCTC", for short (imagine having to say "Corresponding Parts of Congruent Triangles are Congruent" every time you want to use it).
Basically, what CPCTC is trying to say is that if two triangles are congruent, then the corresponding parts are congruent, as well. For example, if triangle ABC is congruent to triangle DEF, we know that angle A is congruent to angle D by CPCTC. We also know that side BC is congruent to side EF by CPCTC. This is clear evidence as to why the order of the letters in a congruence proof, which we learned how to write correctly back two lessons ago, matters - if a congruence proof is not written correctly, then you won't ever be able to tell which parts of the triangles correspond with one another!
And the second most important, but still quite primary, concept that we learned this lesson was the application of everything from day one of being here, sitting in front of a computer screen in this digital class, into proofs involving triangles. The best way for me to explain exactly what this is about is with a picture, and yes, rubric, I'll narrate the picture, too.
The biggest thing that we took out of this lesson was this idea: corresponding parts of congruent triangles are congruent. I know, it's a mouthful; we just call it "CPCTC", for short (imagine having to say "Corresponding Parts of Congruent Triangles are Congruent" every time you want to use it).
Basically, what CPCTC is trying to say is that if two triangles are congruent, then the corresponding parts are congruent, as well. For example, if triangle ABC is congruent to triangle DEF, we know that angle A is congruent to angle D by CPCTC. We also know that side BC is congruent to side EF by CPCTC. This is clear evidence as to why the order of the letters in a congruence proof, which we learned how to write correctly back two lessons ago, matters - if a congruence proof is not written correctly, then you won't ever be able to tell which parts of the triangles correspond with one another!
And the second most important, but still quite primary, concept that we learned this lesson was the application of everything from day one of being here, sitting in front of a computer screen in this digital class, into proofs involving triangles. The best way for me to explain exactly what this is about is with a picture, and yes, rubric, I'll narrate the picture, too.
Here's an example of a problem we did in class this lesson. It's question number three on the assessment (what grade did I get on that again?), taken as a picture directly from my copy of the document. Here, we can see the application of perpendicular bisectors, midpoints, bisectors, perpendicular lines, right angles, the reflexive property, etc. And of course, the topic we've learned in this unit so far. And it wasn't limited to this! There were problems in there somewhere that got the Isosceles Triangle Theorem involved, that got the Third Angles Theorem involved, that got the Triangle Angles Theorem involved.
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That about covers it for this lesson.