Geometric Concepts and Terms

LT 1A: I can explain the difference between undefined concepts (point, line, and plane) and terms (angle, circle, perpendicular line, parallel line, line segment, distance along a line, and distance around a circular arc.) I can draw and explain the definitions of these concepts.

Hook

• What songs would make your top 5 songs of 2013 chart?

• Raise your hand when you hear a mathematical term in the lyrics of this song!

• https://www.youtube.com/watch?v=tsW1G1JlgRU

Investigate

• Draw a visual representation of the following:– Plane X contains points A, B, and C.– intersects at B. The lines are perpendicular.

I. Undefined Concepts

• A. In geometry, point, line, and plane are considered undefined concepts, because they are only explained using examples and descriptions.

I. Undefined Concepts

– 1. Point: An exact location in space (has no size).• We represent points using dots and capital letters.• We name points by their letter.

• 2. Line: Infinitely many points that extend forever in both directions. (always straight)• a. There is exactly one line through any two points.• b. How we name lines• i. by two points on the line• ii. by a lowercase script letter

I. Undefined Concepts

What are all of the ways to

name this line?

• 3. Plane: a flat surface made up of points that extends infinitely (forever) in all directions.– A. There is exactly one plane through any three

points not on the same line.– B. How we name planes

i. capital script (cursive) letter ii. three points not on the same line

I. Undefined Concepts

What are all of the ways to

name this plane?

Term Key Characteristics Diagram

Angle A shape, formed by two lines or rays diverging from a common point (the vertex).

Circle a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

Perpendicular Lines Opposite reciprocal slopes, intersect at right angles

Parallel Lines have the same slope, never intersect

Line Segment a piece of a line that is in between two points, named by endpoints

Distance Along a Line

Distance Around a Circular Arc