Geometry Axioms and Metrics

Geometry Axioms and Metrics

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial covers fundamental concepts in geometry, starting with the existence and incidence axioms. It introduces the ruler postulate, explaining how every line can be seen as a number line with a one-to-one correspondence between points and real numbers. The concept of betweenness is discussed, along with the definition of segments. The video also explores properties of distance, emphasizing algebraic consequences, and introduces various metrics, including Euclidean, taxicab, and spherical metrics.

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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the existence axiom state about points in geometry?

There is more than one point in geometry.

Points do not exist in geometry.

Every point is unique.

There is only one point in geometry.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to the incidence axiom, what do two points determine?

A triangle

A line

A plane

A circle

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main idea of the ruler postulate?

Every line is a triangle.

Every line is a number line.

Every line is a circle.

Every line is a square.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the ruler postulate, what is the distance between two points P and Q?

The sum of X and Y

The product of X and Y

The square of X minus Y

The absolute value of X minus Y

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a one-to-one correspondence mean in the context of the ruler postulate?

No points correspond to numbers.

Each point corresponds to multiple numbers.

Each point corresponds to exactly one number.

Each number corresponds to multiple points.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the concept of betweenness in geometry?

A point is between two others if they form a circle.

A point is between two others if they form a triangle.

A point is between two others if they are collinear.

A point is between two others if they are parallel.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is a line segment denoted in geometry?

AB with a dotted line

AB with a dashed line

AB with an overline

AB with an underline

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