Lesson 2: Basic Concepts of Geometry
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- Lewis McGee
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1 : Basic Concepts of Geometry Learning Target I can identify the difference between a figure notation and its measurements I can list collinear and non collinear points I can find the distance / length of two points on the number line Relevant Vocabulary Geometric Construction: a set of for creating geometric using a - and a. The two most basic types of instructions are: 1. Given any two points A and B, a can be used to draw the line AB or segment AB 2. Given any two points C and B, a can be used to draw the circle that has center at C that passes through B. (Abbreviation: Draw circle: center C, radius CB.) Constructions also include steps in which the points where lines or circles intersect are selected and labeled. (Abbreviation: Mark the point of intersection of the lines AB and PQ by X, etc.) Figure: any on a. Usually the term figure refers to certain common shapes like triangle, square, rectangle, etc. But the definition is broad enough to include any set of points, so a triangle with a line segment sticking out of it is also a figure. Equilateral Triangle: a triangle with three side lengths. Collinear: when or more points are on the line. From the diagram at right, Identify points that are collinear Identify points that are non collinear
2 From the diagram at right, Identify points that are collinear Identify points that are non collinear Notation: This table is clarifies notation and the difference between a figure, and its measurements. Term Figure Notation Measurement Notation Line containing points A and B Line Segment with endpoints A and B Line AB is parallel to line CD AB AB AB CD A line cannot be measured Length of AB = AB or AB N/A Ray with vertex A that contains point B AB A ray cannot be measured Distance between points A and B N/A Dist (A, B) or AB Even though the notation will always make the meaning of each statement clear, it is worthwhile to consider the context of the statement to ensure correct usage. Here are some examples of correct usage: AB intersects AB refers to a line. AB + BC = AC Find AB so that AB CD. AB = 6. Only numbers can be added and AB is a length or distance. Only figures can be parallel and AB is a segment AB refers to the length of the segment AB or the distance from A to B.
3 Here are some examples of incorrect usage: AB + BC = AC AB CD. AB = 6. Only numbers can be added. Line segments are figures not measurements. Only figures can be parallel. AB and CD are measurements (numbers). This would be like saying 4 is parallel to 6. AB refers to a figure. It is not a measurement. Finding distance on a number line: All real numbers are represented on the number line below. This can be thought of as a one-dimensional coordinate system. How could we find the distance between any two points? How could you find the distance between point A and point B? How could we find the distance between point B and point E? All measures of distance and length are positive, regardless of the direction and orientation of the points with respect to one another or that of a line segment. Two points cannot be a negative distance apart. Nor can a line segment have a negative length. This year, we will often be using the concept of TO (as in what position did we go to ) and FROM (as in what position did we start from) when we compare changes in size and position. One definition of distance between points on a number line is expressed by distance = TO FROM
4 : Basic Concepts of Geometry Classwork Collinear Points Exercise 1. A. Name three collinear points on line q and on line s B. Name 2 sets of non-collinear points Exercise 2. Name a point that is collinear with the given points 1. O and S 2. P and R 3. U and T 4. U and S 5. Name 3 points non-collinear with T and V 6. Q and S 7. T and R 8. U and V 9. P and S 10. Name 3 points non-collinear with T and U #1-10 Distance & Length Exercise #3 Figure for # Find the distance between point G and point L 2. Find the distance between point K and point M 3. Find the distance between point A and Point D 4. Find the distance between point B and point F 5. Find the distance between point C and point H 6. Find the distance between point E and point N
5 Distance & Length 7. Find the distance between point L and point A 8. Find the distance between point D and point L 9. Find the distance between point N and point K 10. Find the distance between point K and point H 11. Find the distance between point C and point I 12. Find the distance between point B and point M Exercise# 4 Under what conditions (in terms of distances AB, CD, AC) do the circles A and C have (draw and label a picture) a. One point in common? b. No points in common? c. Two points in common? d. More than two points in common? Why?
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