GEOMETRY IN THE REAL WORLD
Miranda Hyde
POINT
B
A point in the geometry world is a dot
that is ALWAYS labeled with a capital
letter. A good example of a real world
object would be an eyeball. Notice that
in the picture to the right, its labeled with
a capital ‘B’. Don’t forget to label!
http://www.domtesta.com/uploads/userfilesimage/eyeball-with-shadow-on-white-background.jpg
LINE
•M
A line in the geometry world is a straight
line that is infinitely long. It is always
labeled from endpoint to midpoint. A
good example of a real world object is
a highway. A line can either be called by
one point, or multiple points for the
endpoint, to the midpoint, to the other
endpoint or vise versa.
http://www.buffalogov.org/files/Images/highway4.JPG
PLANE
What is a plane? A plane in the
geometry world is a shape that is
labeled with a capital letter. A real
world example of a plane would be a
map. A map has lines, segments, points,
angles, rays, and other geometrical
figures.
http://www.travelchinaguide.com/images/map/beijing/city-map.jpg
M
http://www.wpclipart.com/education/supplies/ruler/ruler_metal_T.png
SEGMENT
•B
What’s a segment? A segment is a
straight line. But be careful when you say
line, because it eventually is stopped by
its two endpoints. Yes, of course my
example is a ruler, and yes the
measurement can keep going, but the
ruler is ended on both sides. You can
always find longer measurement tools
such as a measuring tape, a meter stick,
etc. but, in no way is it possible for this
ruler to grow any.
A•
RAY
A ray? Oh yea, that’s like a line and a
segment combined. It’s infinitely long in
only ONE direction. One end of the ray is
stopped by a point, and the other keeps
going. A good example of a ray in the
real world is the sun. The sun rays keep
going away from the actual sun. The sun
itself is the point.
•P
http://www.wpclipart.com/weather/sun/sun_5/sun_rays_sharp_orange.png
COLLINEAR POINTS
Collinear points are points that all lie on
the same line. Its quite simple, you see, if
the points don’t lay on a line together
than they aren’t collinear. In the real
world example, as you can see, the
freckles are all on the same line which
makes them collinear. All of the other
freckles aren’t collinear to collinear
points. Points, M, D, and H are collinear.
•M
•D
•H
http://fc05.deviantart.net/fs50/i/2009/270/6/6/freckles_by_anapirata.jpg
ACUTE ANGLES
An acute angle is an angle that measures
to be less than 90 degrees. A slice of
pizza is a great real world example
because its definitely acute.
http://images.graphicleftovers.com/11014/item26135/26135_thumb125.jpg
OBTUSE ANGLE
An obtuse angle is an angle that
measures up to 180 degrees but no less
than 90 degrees. A roof is a really good
obtuse angle because it’s a wide angle.
https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcQAWOeqfOuKhUZgHaSQvDExwAmhCeHqWql5h2o5NX854spbtsmt
RIGHT ANGLE
A right angle is an angle that is
absolutely 90 degrees. Cant be any
more or any less. The edge of an iPhone
is a right angle. To know that it’s a right
angle for sure, there is usually a box in
the middle of the angle.
http://www2.pcmag.com/media/images/302835-apple-iphone-5-sprint.jpg
PERPENDICULAR LINES
Perpendicular lines are 4 sets of 9
degree angles. A baseball field is a real
world example of perpendicular lines.
The lines are the perpendicular lines, and
the bases are the points.
http://penguinsandpeacocks.wikispaces.com/file/view/perpendicular_l
inesbball.jpg/234981138/616x234/perpendicular_linesbball.jpg
COMPLEMENTARY ANGLES
Complementary angles are angles that
add up to be 90 degrees. A clock can be
complementary at times. A
complementary angle shares a common
ray like an Adjacent angle.
http://1.bp.blogspot.com/-t7iH1e3EmAo/TpnbYr5_pBI/AAAAAAAAACU/u35_6sXSEvM/s1600/DSCF6433.JPG
SUPPLEMENTARY ANGLES
Supplementary Angles are the opposite
of Complementary Angles. Instead of
adding up to be 90 degrees, they add
up to be 180 degrees. A highway that
has a little back road coming out of the
side of it is a GREAT example from the
real world for supplementary angles.
•A
•B
•C
http://image.mathcaptain.com/cms/images/88/acute-angle-real-life-1.jpg
VERTICAL ANGLES
Vertical angles are a pair of nonadjacent angles formed when two lines intersect.
Vertical angles are all around the world. A good
real world example is an open pair of scissors.
ACUTE TRIANGLE
An acute angle is a triangle and each angle is
acute. An acute angle is an angle that measures
less than ninety degrees but more than zero
degrees. An equilateral triangle is an acute angle.
OBTUSE TRIANGLE
An obtuse triangle is a triangle that has one
angle that measures more than 90 degrees but less
than 180 degrees. Obtuse triangles are literally all
over the real world. Obtuse angles have one obtuse
angle and two acute angles. Nothing is congruent in
an obtuse angle.
EQUILATERAL TRIANGLE
An equilateral triangle is a triangle with all three
sides of equal length. All the angles are 60°. An
equilateral triangle is also an isosceles triangle.
Equilateral triangles are all around in the real
world. A good example is a pool triangle.
ISOSCELES TRIANGLE
An isosceles triangle is a triangle with two
congruent angles, which also means two of the sides
are congruent. As you can see in the picture shown
to the right, the red triangle is an isosceles triangle
because two angles are congruent as well are two
sides.
SCALENE TRIANGLE
A scalene triangle means that each angle/side of
the triangle in UNcongruent. No angles are the
same and no sides are the same. All these math
terms are seen all over the real world all the time.
RIGHT TRIANGLES
A right triangle has 1 right angle in it because a
triangle cant have two. A right angle is exactly 90
degrees every time. Usually a right angle is
labeled with a box. Most popular right triangles
are, 90, 45, and 45, or 90, 60, and 30. This bird
house is a right triangle. To solve a missing angle in
a right triangle, you use a method called the
Pythagorean Theorem. “A+B=C”. C stands for the
hypotenuse. A and B are the other angles.
CIRCLES
The diameter of a circle is the measure straight
across the middle of the circle. The radius is half of
the diameter. If a line is tangent to a circle, it is
perpendicular to the radius drawn to the point of
tangency. In geometry, a secant line of a curve is a
line that (locally) intersects two points on the curve.
A chord is an interval of a secant line, the portion
of the line that lies within the curve. The
word secant comes from the Latin word secare,
meaning to cut.