Warm-Up
A picture of 16 number cubes is shown. What do you notice? On your whiteboard, find the sum of the number cubes. Show your work or explain your thinking.
If all of the number cubes with 3 dots were changed to number cubes with 6 dots, how would you find the new sum? Show your work or explain your thinking.
Intro to Euclidean Geometry
Unit 1.2
start
LEARNING Target
Distinguish between definition, postulate, and theorem.
Understand the role of a proof.
Relate properties of equality to the properties of congruence.
What is Euclidean Geometry?
Euclidean Geometry is the study of planes and solid figures on the basis of axioms and theorems compiled by the Greek Mathematician Euclid. Rather than using algorithms to solve problems like you may have done in other math courses, Euclidean Geometry emphasizes using facts, ideas, and assumptions.
What is Euclidean Geometry?
Each of Euclid’s 13 books have proofs. Each proof shows how a hypothesis is true. The proof uses definitions, postulates, and proven theorems to explain why the hypothesis is true.
The first postulate of Euclid's Book 1 is shown:
A straight line segment be drawn joining any two points.
1. Use a straightedge to show the postulate using the points shown:
2. Discuss with your partner why a postulate is something that is self-evident. Summarize your discussion.
Let's Prove Vertical Angles Theorem (that vertical angles are congruent)
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FOLDABLE NOTES
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Intro to Euclidean Geometry
Leilani Velazquez
Created on October 7, 2022
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Transcript
Warm-Up
A picture of 16 number cubes is shown. What do you notice? On your whiteboard, find the sum of the number cubes. Show your work or explain your thinking.
If all of the number cubes with 3 dots were changed to number cubes with 6 dots, how would you find the new sum? Show your work or explain your thinking.
Intro to Euclidean Geometry
Unit 1.2
start
LEARNING Target
Distinguish between definition, postulate, and theorem.
Understand the role of a proof.
Relate properties of equality to the properties of congruence.
What is Euclidean Geometry?
Euclidean Geometry is the study of planes and solid figures on the basis of axioms and theorems compiled by the Greek Mathematician Euclid. Rather than using algorithms to solve problems like you may have done in other math courses, Euclidean Geometry emphasizes using facts, ideas, and assumptions.
What is Euclidean Geometry?
Each of Euclid’s 13 books have proofs. Each proof shows how a hypothesis is true. The proof uses definitions, postulates, and proven theorems to explain why the hypothesis is true.
The first postulate of Euclid's Book 1 is shown:
A straight line segment be drawn joining any two points.
1. Use a straightedge to show the postulate using the points shown:
2. Discuss with your partner why a postulate is something that is self-evident. Summarize your discussion.
Let's Prove Vertical Angles Theorem (that vertical angles are congruent)
Lorem ipsum dolor sit amet
Lorem ipsum dolor sit amet
Lorem ipsum dolor sit amet
Lorem ipsum dolor sit amet
FOLDABLE NOTES
Document Camera
start