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- 1. GeometryGeometry • the branch of mathematics that is concerned with the properties of configurations of geometric objects – points, (straight) lines, and circles.
- 2. GeometryGeometry • The word ‘geometry’ comes from the Greek words geo, meaning earth, and metria, meaning measure.
- 3. A Greek mathematician who lived around the year 300 BC is often referred to as the Father of Geometry for his amazing geometry works that included his influential book, ‘Elements’.
- 4. Types of GeometryTypes of Geometry • Plane geometryPlane geometry deals with objects that are flat, such as triangles and lines, that can be drawn on a flat piece of paper in two dimensions. • Solid geometrySolid geometry deals with objects in that space, having width, depth and height, such as cubes and spheres.
- 5. Tools of GeometryTools of Geometry • The compass and straight edge were powerful tools in the advancement of geometry, allowing the construction of various lengths, angles and geometric shapes.
- 6. Geometry in Real LifeGeometry in Real Life
- 7. Geometry in ActionGeometry in Action • Design and manufacturing – Architecture – Assembly planning – CAD/CAM – Robotics – Modeling – Textile layout – VLSI design • Graphics and visualization – Computer graphics – Graph drawing – Virtual reality – Video game programming
- 8. Geometry in ActionGeometry in Action • Medicine and biology – Medical imaging – Biochemical modeling • Information systems – Cartography and geographic information systems – Data mining and multidimensional analysis • Physical sciences – Astronomy – Molecular
- 9. CAD/CA M Architectu re VLSI design Textile layout Biomedical imaging Cartograph y Molecular modeling
- 10. Lines, Points andLines, Points and PlanesPlanes
- 11. PointsPoints • A point has no dimension. • It is usually represented by a small dot. A
- 12. LinesLines • A line extends in one dimension. • It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. Line l or AB B l A
- 13. LinesLines • Collinear points are points that lie on the same line. • Points A, B, and C are collinear. C Line l A B
- 14. LinesLines • The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. C Line l A B A B Segment AB
- 15. LinesLines • The ray AB (symbolized by BC) consists of the initial point B and all points on Line l that lie on the same side of B as point C. C Line l A B CB Ray BC
- 16. PlanesPlanes • A plane extends in two dimensions. • The plane extends without end even though the drawing of a plane appears to have edges. A B C M
- 17. PlanesPlanes • A plane extends in two dimensions. • The plane extends without end even though the drawing of a plane appears to have edges. A B C M • Coplanar points are points that lie on the same plane.
- 18. PlanesPlanes • D, E, F, and G lie on the same plane, so they are coplanar. • D, E, F, and H are also coplanar; although, the plane containing them is not drawn. G D E F H
- 19. PlanesPlanes A line intersects a plane in one point.
- 20. PlanesPlanes Two planes intersect plane in a line.
- 21. Parallel Lines,Parallel Lines, Transversals andTransversals and AnglesAngles
- 22. Parallel LinesParallel Lines Two lines are parallel lines if they are coplanar and do not intersect.
- 23. Parallel PostulateParallel Postulate • If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. ll PP
- 24. TransversalTransversal A line that intersects two or more coplanar lines at different points. P1 P2
- 25. Transversal and AnglesTransversal and Angles • Angle 1 and 5 are corresponding angles • Angles 1 and 8 are alternate exterior angles • Angles 3 and 5 are alternate interior angles. 1 2 5 6 7 8 3 4 • Angles 3 and 5 are consecutive interior angles.
- 26. Corresponding AnglesCorresponding Angles PostulatePostulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 2 1 l m If l // m, then ∠ 1 ≅ ∠ 2.
- 27. Alternate Interior AnglesAlternate Interior Angles TheoremTheorem If two parallel lines are cut by a transversal, then the pairs of alternate interior ∠s are ≅. 2 1 l m If l // m, then ∠1 ≅ ∠2.

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