Geometric Concepts and Terms LT 1A: I can explain the difference between undefined concepts (point, line, and plane) and terms (angle, circle, perpendicular.

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Presentation transcript:

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!

Investigate Draw the following description: A line including points A and B lies in a plane. A line including points B and C is perpendicular to the line containing points A and B.

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?

TermKey CharacteristicsDiagram 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 straight line distance, given by formula Distance Around a Circular Arc distance around a curved arc (given by 2∏r (angle/360)

II. Terms Collinear: Points that lie on the same line are collinear. Coplanar: Points or lines that lie on the same plane are coplanar. Skew: Lines that are neither parallel nor intersect are skew. They lie in different planes. 9 Which points are collinear?

10 III. Let’s Practice I do: Describe the following diagram using mathematical vocabulary:

11 III. Let’s Practice We do: –Name: a pair of parallel lines »a pair of perpendicular lines »two parallel planes

12 III. Let’s Practice I do: Write a description of the following: