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## Warm-Up 2/1/13

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**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**Line Segment**Line Segments, Rays, Parallel Lines and Planes • Definition: A segment is a part of a line consisting of two endpoints and all points between • Names: or**Ray**• Definition: A ray is the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.**Name three segments.**• Name four different rays. • Name two opposite rays.**Perpendicular Lines: lines that intersect to form right**angles.**What are Parallel Lines?**Are you sure you have the correct definition? Definition: Parallel Lines are coplanar lines that do not intersect What other type of lines do not intersect????**Skew Lines**Definition: Skew Lines are noncoplanar lines that do not intersect Are there any in the classroom?**Name the segments parallel to:**Name a pair of skew lines.**Parallel Planes:**Parallel Planes: planes that do not intersect. EX. Top ll bottom HGFE ll DCBA**Homework**• 1-3 Segments, Rays, Parallel Lines and Planes Worksheet • Quiz Wednesday!