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Geometry and Measurement of Plane Figures Euclid’s Muse Transparencies/ Blackline Masters GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Muse Directions First: • Draw and label three columns on your chart paper as shown below. Name Picture Definition • Tape your cards to the chart paper (3 per page) in the appropriate columns. • Name the shape and write a definition if the card is a picture. • Draw a picture and write a definition if the card is a name. • Name the shape and draw a picture if the card is a definition. GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Muse Directions First: • Draw and label three columns on your chart paper. • Tape your cards to the chart paper (3 per page) in the appropriate columns. • Name the shape and write a definition if the card is a picture. • Draw a picture and write a definition if the card is a name. • Name the shape and draw a picture if the card is a definition. Second, as a group: • Rotate to the next table and check the pictures and definitions. • Put an asterisk, using your group pen, if you agree with a name, picture, and definition. • Put an “M” if you disagree with any part and, using your group pen, write your modification or correction. • Put a question mark if you have a question or would like to discuss the item. • Repeat the rotation until you have reviewed all the charts. * We agree with the name, picture, and definition. M We disagree or want to add something. Our Modifications appear in our group color. ? We would like to discuss or have questions about this item. GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Biography Euclid is thought to have been a Greek mathematician who taught in Alexandria around 300 B.C. It is possible that he was the founder of its most famous mathematical school. Some theories suggest that his name is applied to the work of a group of mathematicians that made up the school. Euclid is best known for the multivolume Elements, the most widely known mathematical books of classical times—books still used in many geometry classes today. “ . . . he introduces quite a number of definitions . . .” Indeed, Elements begins with definitions and postulates. GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Sample Definitions A straight line is a line that lies evenly with the points on itself. A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another. A diameter of a circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle. Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle is that which has two of its sides alone equal, and a scalene triangle is that which has its three sides unequal. GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Muse: Words and Definitions 1. acute triangle a triangle in which each of the three angles is less than 90º 2. altitude a line segment that shows the height of a figure; or, in a triangle, the line segment drawn from the vertex of an angle perpendicular to the opposite side 3. angle a geometric figure made of two rays or two line segments that share the same endpoint, called a vertex 4. circle the set of all points in a plane that are equidistant from a given point 5. circumference the distance around a circle 6. congruency having the same shape and size 7. degree a unit for measuring angles; 360 of these make a complete revolution around a point 8. diameter the line segment passing through the center of a circle and connecting two points on the circumference of a circle 9. hypotenuse the side of a right triangle that is opposite the right angle 10. isosceles triangle a triangle with two congruent sides 11. line a set of points that form a straight path in two directions that are opposite each other 12. obtuse triangle a triangle that has one angle greater than 90º 13. octagon a polygon with eight sides GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development Euclid’s Muse: Words and Definitions continued 14. parallelogram a quadrilateral with opposite sides that are parallel 15. pentagon a polygon with five sides 16. perpendicular meeting at right angles 17. plane a flat surface that extends forever in all directions 18. plane figure a geometric shape that lies entirely in one plane 19. polygon a closed figure made of three or more sides or line segments 20. quadrilateral a polygon with four sides 21. radius the line segment from the center of the circle to a point on its circumference 22. ray a part of a line that includes one endpoint and extends out from that point indefinitely 23. rectangle a quadrilateral with four right angles 24. regular polygon a polygon with all sides congruent and all angles equal 25. right triangle a triangle that has an angle of 90º 26. scalene triangle a triangle that has no congruent sides 27. square a regular, four-sided polygon GEOMETRY AND MEASUREMENT OF PLANE FIGURES—EUCLID’S MUSE Copyright© 2002 by the McGraw-Hill Companies—McGraw-Hill Professional Development