Warm-Up 2/1/13 Describe any points, lines and planes you see in this picture
Unit 2: Introduction to Geometry • Essential Question: • How do the basic properties of geometry apply to the real world? How do you use deductive reasoning, logic, and mathematical properties to help you draw conclusions? • Bonus Question: • Write real-world examples of conditionals and converses that meet the following criteria, and explain each answer. • A) Write a conditional that is true but whose converse is false. • B) Write a true conditional whose converse is also true.
Point Points, Lines, and Planes Definition: A point is an indication of a location. A point has no size. A point is represented by a small dot and is named by a capital letter Example: Name: Point A A
Line Definition: A line is a series of points that extends in two opposite directions without end. You can name a line by any two points on the line. Another way to name a line is with a single lowercase letter. Names: **must be only two points**
Collinear points Definition: Collinear points are points that lie on the same line. In the picture below, points A and B are collinear but C is not Name the collinear points: B A C
Plane Definition: A plane is a flat surface that has no thickness. A plane contains many lines and extends without end in the directions of all its lines. You can name a plane by either a single capital letter or by at least three of its non-collinear points. Vertical • Horizontal Plane Plane A C B P
Plane • Names:
Coplanar Definition: Points and lines in the same plane are coplanar. M P
Space: Space is the boundless, three-dimensional set of all points
Intersection Intersection: the set of points that two figures have in common.
Basic Postulates of Geometry (A Postulate is a rule accepted as true without proof) Draw two points and connect the points. What is the geometric figure.
Postulate 1-1 • Through any two points there is exactly one line. • Line t is the only line that passes through points A and B. t B A
Postulate 1-2 • If two lines intersect, then they intersect in exactly one point • AE and BD intersect at C A B C D E
Postulate 1-3 • If two planes intersect, then they intersect in exactly one line. • Plane RST and plane STW intersect in ST R T S W
Postulate 1-4 • Through any three noncollinear points there is exactly one plane
a) Name the plane on the bottom of the box • b) Shade the plane that contains E, H, and C. • c) Name another point that is in the same plane of point A, B, and C. • d) Name another point that is coplanar with points E, H, and C. • e) Are points A and G collinear?
2. Name the intersection of… A. Planes HGF and GCB GF B. Planes HDC and DAB DC C. Planes EHD and FGC None
d. Plane EFB and Point B e. Plane HEB and Point C f. Plane HEF and Point F
Homework • Practice 1-2 • Quiz Wednesday!