Cogito
Geometry · Chapter 1 · Lesson 1
Definitions, Postulates, and Proof
What counts as an argument.
8 problems · about 19 minutes · G-CO.A.1, G-CO.C.9
What this lesson teaches
The student distinguishes definitions, postulates, and theorems, and writes a short deductive argument.
- Point, line, and plane are undefined terms.
- A postulate is accepted; a theorem is proved.
- Every line of a proof carries a reason.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSupplementary to 118°?
Answer 62
Why 62°.
What must every line of a proof have?
Answer A reason.
Why Every step needs a justification.
Complementary to 32°?
Answer 58
Why 90 − 32.
Supplementary to 91°?
Answer 89
Why 180 − 91.
Build It Up
The same ideas with more to keep track of.
2 problemsIs "point" a defined term?
Answer No. It is undefined.
Why Everything else is built from it.
Two vertical angles, one is 47°. The other?
Answer 47
Why Vertical angles are equal.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Supplement: Two supplementary angles, one is 55°. What is the other?
Answer 125 degrees
Why 125°.
The Vocabulary: A statement accepted without proof is called what?
Answer A postulate.
Why A postulate.