Download Angles

Math » Unit 3 - Geometry Explorations
Unit 3 - Geometry Explorations
Unit 3: Geometry
Brainpop's Introduction to Geometry: History of geometry, introduction to terms:
point, line, dimensions, plane, line segment, compass, protractor,
Lines
Brainpop's Parallel & Perpendicular Lines
Angles
TV411's Angles on the Move: students use an online protractor to measure angles
Brainpop's Measuring Angles: vertex, naming angles, rays, acute, right, obtuse, straight
angles, supplementary angles, complimentary angles
Math Playground's Alien Angles Alien Angles :students estimate angles to launch space
blobs and defeat aliens.
Polygons
Brainpop's Polygons: Intro to polygons, using vocab: line segment, vertices, regular vs.
irregular polygons
Brainpop's Types of Triangles: triangles classified by sides or angles; equilateral, isosceles,
scalene, hypotenuse, legs, acute triangles, obtuse triangles
Brainpop's Similar Triangles: Intro to "indirect measurement" using similar triangles
Transformation of Polygons
BBC's Bathroom Tiles: 3 levels of games teaching transformations
Brainpop's Transformation: Introduction to Translation, rotation, reflection
Perimeter & Area
Brainpop's Area of Polygons: area of rectangles, parallelograms, trapezoids
Word
Definition

this section contains information that students will
use as they take an imaginary world tour.


plastic device with many uses
ruler, half circle protractor, full circle protractor,
percent circle, pattern block shapes


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.
World Tour
Geometry
Template
Point



Line Segment


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

a strip of wood, plastic, or metal that may be used to
draw a straight line.

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
Straightedge
Ray

Line

a straight path that goes on forever in both
directions

Angle



Right angle



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

an angle that measures between 0 degrees and 90
degrees

an angle that measures between 90 degrees and 180
degrees

measures 180 degrees

an angle that measures greater than 180 degrees
and less than 360 degrees

angles that are next to each other and share a side
and common vertex

when two lines intersect each other 4 angles are
formed. The angles "opposite" each other are called
vertical angles or opposite angles

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
Acute angle
Obtuse angle
Straight angle
Reflex angle
Adjacent angles
Opposite or
Vertical angles
Polygon
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



a polygon whose sides are all the same length and
whose angles are all equal

all vertices are pushed out

at least one vertex is pushed in
Triangle


a polygon with three sides and three angles
the measure of all the angles equals 180 degrees
Right Triangle


a triangle with one right angle
the angle looks like the corner of a square


a triangle with 3 equal side and 3 equal angles
it is a regular polygon
Isosceles
triangle



at least two sides are the same length
an equilateral triangle is also an isosceles triangle
can be a right triangle
Scalene triangle


no sides are the same length
can be a right triangle
Congruent


a figure that is an exact copy
has the same size and shape



a polygon with 4 sides
the measure of the 4 angles equals 360 degrees
also called a quadrilateral


a quadrangle with 4 equal sides and 4 right angles
also considered a parallelogram, a rectangle, and a
rhombus


a parallelogram that has 4 equal sides
the angles are not right angles
Regular polygon
Convex
Concave
Equilateral
triangle
Quadrangle
Square
Rhombus
Rectangle


a parallelogram with 4 right angles
opposite sides are equal in length
Parallelogram


a quadrilateral with 2 pairs of parallel sides
opposite sides are parallel



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



a quadrangle with 2 pair of equal sides
the equal sides are next to each other
not a parallelogram


lines or segments on a flat surface that never meet
like railroad tracks

lines or segments that cross each other

lines or line segments that cross and form a right
angle


curved line that forms a closed path on a flat circle
not a polygon

all of the points on a circle will be the same distance
from the center

tool used to draw circles

any line segment that connects the center of the
circle with a point on the circle

any line segment that passes through the center of
the circle and has both of its endpoints on the circle

circles with the same center that do not cross
Trapezoid
Kite
Parallel lines
Intersect
Perpendicular
Circle
Center of a
circle
Compass
Radius
Diameter
Concentric
Inscribed
Square
Tessellations

a square whose vertices all lie on a circle

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.

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
Always label with upper case letters with the vertex in
the middle.
Angles
Look at the angle and ask yourself "What makes
sense?" Is the angle smaller or larger than a right
angle?
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)
Protractor
Pattern Block
Angles
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
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