Unit 3: Geometry
Word
Definition
World Tour
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this section contains information that students will use as they take an
imaginary world tour.
Geometry
Template
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plastic device with many uses
ruler, half circle protractor, full circle protractor, percent circle, pattern
block shapes
Point
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a location in space
you make a dot with your pencil to show where a point is
upper case letters are used to name points.
Line Segment
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is made up of 2 points and the straight path between them
you can use any tool with a straight edge to draw the path between
the two points.
the two points are called endpoints of the line segment
the points are labeled with upper case letters
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Straightedge
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a strip of wood, plastic, or metal that may be used to draw a straight
line.
Ray
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a straight path that has a starting point and goes on forever in one
direction
the end point is always the first letter in the name of the ray
Line
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a straight path that goes on forever in both directions
Angle
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formed by 2 rays or two line segments that share the same endpoint.
the vertex is where the two segments meet
the rays or segments are called the sides of the angle
when naming an angle the vertex is always in the middle
Right angle
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an angle that measures 90 degrees
forms the corner of a square
a small square is drawn in the vertex of the angle indicating it is a
right angle
Acute angle
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an angle that measures between 0 degrees and 90 degrees
Obtuse angle
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an angle that measures between 90 degrees and 180 degrees
Straight angle
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measures 180 degrees
Reflex angle
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an angle that measures greater than 180 degrees and less than 360
degrees
Adjacent angles
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angles that are next to each other and share a side and common
vertex
Opposite or
Vertical angles
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when two lines intersect each other 4 angles are formed. The angles
"opposite" each other are called vertical angles or opposite angles
Polygon
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a closed figure that is made up of line segments joined end to end
the line segments do not cross
can have any number of sides as long as it has three
Regular polygon
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a polygon whose sides are all the same length and whose angles are
all equal
Convex
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all vertices are pushed out
Concave
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at least one vertex is pushed in
Triangle
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a polygon with three sides and three angles
the measure of all the angles equals 180 degrees
Right Triangle
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a triangle with one right angle
the angle looks like the corner of a square
Equilateral
triangle
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a triangle with 3 equal side and 3 equal angles
it is a regular polygon
Isosceles triangle
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at least two sides are the same length
an equilateral triangle is also an isosceles triangle
can be a right triangle
Scalene triangle
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no sides are the same length
can be a right triangle
Congruent
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a figure that is an exact copy
has the same size and shape
Quadrangle
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a polygon with 4 sides
the measure of the 4 angles equals 360 degrees
also called a quadrilateral
Square
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a quadrangle with 4 equal sides and 4 right angles
also considered a parallelogram, a rectangle, and a rhombus
Rhombus
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a parallelogram that has 4 equal sides
the angles are not right angles
Rectangle
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a parallelogram with 4 right angles
opposite sides are equal in length
Parallelogram
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a quadrilateral with 2 pairs of parallel sides
opposite sides are parallel
Trapezoid
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a quadrangle that has only one pair of parallel lines
it is not a parallelogram
the 4 sides can all be of a different length
Kite
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a quadrangle with 2 pair of equal sides
the equal sides are next to each other
not a parallelogram
Parallel lines
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lines or segments on a flat surface that never meet
like railroad tracks
Intersect
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lines or segments that cross each other
Perpendicular
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lines or line segments that cross and form a right angle
Circle
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curved line that forms a closed path on a flat circle
not a polygon
Center of a circle
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all of the points on a circle will be the same distance from the center
Compass
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tool used to draw circles
Radius
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any line segment that connects the center of the circle with a point on
the circle
Diameter
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any line segment that passes through the center of the circle and has
both of its endpoints on the circle
Concentric
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circles with the same center that do not cross
Inscribed Square
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a square whose vertices all lie on a circle
Tessellations
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a n arrangement of repeated, closed shapes that cover a surface so
that no shapes overlap, and there are no gaps between shapes
shapes that tessellate-square, equilateral triangle, hexagon.
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Notes and Helpful Hints
Topic
Properties of
Polygons
Notes
Polygons can have more than one property, in fact they may have many.
For example: a square has 4 right angles, 4 equal sides, is a
parallelogram, is a regular polygon, is a quadrilateral.
Parallelograms:
square, rectangle, rhombus
Not parallelograms:
trapezoid, kite
Perimeter:
add up the length of all the sides
*Remember in a regular polygon all the sides are the same length (even
if they are not marked on all the sides)
*In a rectangle the opposite sides are equal (don't forget to add all of
them up)
Area:
Square and rectangle: length of the base X the height Formula A=b X h
Triangle: length of the base X the height divided by 2 Formula A= b X h
divided by 2.
Circle:
*always mark the center of your circle when drawing it with a compass.
This way if the compass slips you know where to replace it.
Circle measures 360 degrees
Circumference: (really the perimeter of the circle) Formula: C= 3.14 (pie)
X diameter
Angles
Always label with upper case letters with the vertex in the middle.
Look at the angle and ask yourself "What makes sense?" Is the angle
smaller or larger than a right angle?
Protractor
Always estimate before you measure, it will help you make sure you
are reading the correct measurement for the angle. Ask yourself what
type of angle do I have? (acute, obtuse, right, straight, reflex)
Half-circle: line up one of the sides of the angle with zero making sure the
vertex is in the correct spot
Full-circle: line up one of the sides with the zero and read clockwise.
* If the side of the angle is too short to reach edge of the protractor
extend it with a straightedge
Pattern Block Angles Triangle: angles must add up to 180 degrees, in an equilateral triangle all
the angles measure 60 degrees
Quadrilateral: angles must add up to 360 degrees
Hexagon: angles measure 120 degrees