Download Geometry and Measurement of Plane Figures Euclid`s Muse

Geometry and Measurement
of Plane Figures
Euclid’s Muse
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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