1. Y
M
IN CH
Y
R LD A FREN
T
E R LIZ
M O
E O W
G
Block 3
Geometry H, T3 & T4
2012

2. Explanation
Geometry is not a concept only used in math class, it
simply helps us identify real world applications of
things like shapes and lines. We can use the lessons
we learn in class to discover new things about the
world around us. For example, a stop sign is a
octagon, a regular polygon. The legs of tables and
chairs will often be parallel lines. This PowerPoint will
show examples of Geometry I found in my life. I will
explain how each picture is an example of Geometry
and where I found it.
2

3. Decorative Plate – Circle (L. 23)
This is a picture of a
decorative plate that hangs
in my house.
The plate is an example of a
circle. The center point
(Point A) of the circle was
used in the design by the
artist to determine where to
paint the birds.
Definitions:
A center of a circle is the point inside a circle that is
equidistant from every point on the circle.
A circle is a closed plane curve consisting of all points at a
given distance from a point within it called the center. 3

4. Table Lamp – Decagon (L. 15)
This is a stain glass table
lamp that sits next to the
reading chair upstairs in my
computer room.
This lamp is a regular
decagon. On the lamp, the
congruency of the sides is
shown with pink congruency
markings, the diagonals,
forming central angles are
marked with blue, and the
sides are yellow.
Definitions:
A decagon is a ten-sided polygon.
A regular polygon is a polygon that is both equilateral (all
the sides are the same length) and equiangular (all the
4
angles are the same measure).

5. Stove Fan – Frustum of a Pyramid (L.103)
This picture is of the fan
above my stove, which is used
to bring better air circulation
when cooking food that
produces a lot of smoke.
The red lines represent the
shape of the fan, which
creates a frustum. The blue
lines signify where the top of
the pyramid would be, if it
were complete.
Definitions:
A frustum of pyramid is a part of a pyramid with two
square parallel bases.
In t e r e s t in g N o t e *
A pyramid is a polyhedron formed by a polygonal base and
V o lu m e o f a F r u s t u m : 5
triangular lateral faces that meet at a common vertex.
V = 1/3 h ( B 1 + √ B 1( B 2 ) +

6. Back Yard Fence – Perimeter (L. 19)
At my house, there is a square
back yard. Each side of the yard
is 40 ft. Around that yard, There
is a wooden fence, which is
shown in the picture here.
However, there is a 4 foot
pathway
The fence represents the
perimeter of the yard, which in a
square can be found with the
formula “P = 4s” where s is the
length of the sides, in the case
Working out40 ft.
of my yard, the Formula: Definitions:
Step 1: P = 4s – 4 A perimeter is the sum of the side lengths of a closed
Step 2: P = 4(40) – 4 plane figure.
Step 3: P = 160 – 4
6
Step 4: P = 156 ft

7. Coat Hanger – Rhombus (L.52)
This is a coat hanger that I
use daily in my room to hang
clothes on.
When pulled apart, the coat
hanger forms a rhombus.
The diagonals of the
rhombus bisect each other,
forming congruent segments
and right angles.
Definitions:
A rhombus is a quadrilateral with four congruent sides.
The Properties of a Rhombus state that the diagonals of a rhombus
are perpendicular and that each diagonal of a rhombus bisects
opposite angles. Because opposite angles of a rhombus are equal, 7
when they are bisected by a diagonal, four congruent angles result.

8. CD Case – Tangent (L. 43)
This is a picture of a blank CD
waiting to be used on my
computer desk.
The edge of the CD case, Line
Segment AB which is
represented in yellow, lies
tangent to Circle P,
represented in red around the
CD. The point of tangency in
this picture is Point C.
Definitions:
The tangent of a circle is a line in the same plane as the circle that
intersects the circle at exactly one point.
The point of tangency is the single point that the tangent line
intersects a circle with. 8

9. Nesting Boxes – Ratios (L. 41)
This is a picture of some
nesting boxes that I
received as a gift.
The boxes are similar
shapes because the sides
are equivalent ratios. The
square of the side lengths
of the square top to the
height is ¾.
For instance, a proportion
of these numbers would
be: 6/8 = 4.5/6 = 3/4 =
1.5/2.
Definitions:
A ratio is a comparison of two quantities by division.
Similar polygons are polygons whose corresponding angles are congruent
and whose corresponding sides are proportional.
A proportion is a statement that two ratios are equal. 9

10. Window – Plane Intersections (L. 4)
This is a window on the second
story of my house, looking out
into my front yard.
In this picture, there are 8
planes. 3 are highlighted as
plane M, plane R, and plane P.
Plane M and Plane P intersect
at line segment AB. Planes M,
R, and P intersect at a point,
Point A.
Postulate 7: If two planes intersect, then their intersection is a line.
Definitions:
A plane is an undefined term in geometry; a flat surface that has no
thickness and extends infinitely.
10

11. Mirror and Door – Chord (L.43)
This is a picture of a mirror in
my house that is reflecting a
closet door.
The seam of the closet door,
represented by line segment
AB, is a chord to the circle of
the mirror, represented as
Circle P because points A and
B lie on the circle.
Definitions:
A chord is a segment whose endpoints lie on a circle.
11

12. Porch Railing – Parallel and Perpendicular Lines (L. )
This is a picture of the
wooden railing on my porch.
The poles represent line
segments AE, BF, CG, and DH.
These line segments are
parallel, as signified by the
white markings. The white
right angles show that line
segment AD is perpendicular
to line segments AE, BF, CG,
and DH.
12

13. Rain Gauge – Rectangular Prism (L. 59)
This is a (broken) rain gauge that I have
placed outside to measure the amount of
rainfall.
The rain gauge is in the shape of a
rectangular prism. It has a two bases, one at
the top and one at the bottom, and four
equivalent sides.
To find the volume of this prism, you would
use the formula V = Bh, where B is the area
of one base and h is the volume.
To find the surface area, you would use the
formula SA = ph + 2B, where p is the
Working out Volume: of Workingbase, h Area: the Definitions: and B
perimeter the out Surface is height,
is the area of one base.
Step 1: V = Bh Step 1: SA = ph + 2B
A rectangular prism is a prism with six rectangular faces.
Step 2: V = 1(1.5)(7) Step 2: SA = 2(1 + 1.5)(7) + 2(1)
(1.5) Volume is the number of non-overlapping unit cubes of a given
Step 3: V = 10.5 in ² size that will exactly fill the interior of a three-dimensional figure.
Step 3: SA = 2(2.5)(7) + 2(3)
Step 4: SA = 41 in Surface Area is the total area of all faces and curved surfaces of a
three-dimensional figure.
13

14. Macaroni Box – Nets (Investigation 5)
This is a deconstructed macaroni
box, found in my recycling and the
box in its completed form, found
in the pantry.
The deconstructed box is a net of
the original box. The single plane
deconstruction could be folded to
form the original box. The yellow
sections of the net correspond to
the yellow sections of the box, the
red to the red, and the blue to the
blue.
Definitions:
A net is a diagram of the faces of a three-dimensional figure,
arranged so that thee diagram can be folded to form the three-
dimensional figure. 14

15. Scented Candle – Cylinder (L. 62)
This is a scented candle that my
mother keeps on the kitchen
counter.
The candle is in the shape of
cylinder. The height of the candle is
15 cm, and the radius, or distance
from the center point of the circle
base, which is the wick, to the edge
of the candle is 5 cm.
To find the volume of the cylinder,
you use the formula V = πr²h.
To find the Surface Area, the formula
SA = 2πrh + 2B is used. The variable
h represents the height, B
represents the oareag of uthe base, and
W o r k in g o u t W r k in o t
Definition:
Vo lu m e : Surfa c e Ar e a :
r represents the radius.
S t e p 1: V = π ² h
r S t e p 1: S A = 2 π h +
r A cylinder is a three-dimensional figure with two parallel
2 B
S t e p 2 : V = π ² ( 15 )
5 congruent circular bases and a curved lateral surface
Step 2 : SA = that connects the bases.
Step 3 : V = π2 5 )
(
2 π ( 1 5 ) + 2 π5²
5
( 15 ) 15
S t e p 3 : S A = 15 0 π +
Step 4 : V = π3 7 5 )
(
2 π25

16. Stairs – Kite (L. 19, L. 69)
This is a segment of my stairway,
enabling the stairs to curve
around the wall.
The shape of the step outlined in
yellow is a kite. The dotted lines
represent the hidden parts of the
shape, as it was impossible to
capture the entire shape from any
angle. Two pairs of the kite are
congruent and its diagonals form
four right angles.
P r o p e r t ie s o f
K it e s : Definitions:
A kite is a quadrilateral with exactly two pairs of
T h e d ia g o n a ls congruent consecutive sides. 16
o f a k it e a r e
p e r p e n d ic u la r .

17. Salt Shaker – Regular Polygons (L. 15 )
This is an aerial view of a
salt shaker that I found on
my kitchen table.
The base of the salt
shaker forms a regular
octagon. The eight sides of
the octagon are marked
with red lines and yellow
congruency markings, and
the angles are marked
with blue.
Definitions:
A regular polygon is a polygon (a closed plane figure formed
by three or more segments) that is both equiangular and
equilateral. 17

18. Garden Gate – Special Right Triangles (L. 53, L.56)
This is a picture of a gate that my
father had built surrounding his
garden to protect it from animals
that would eat his plants.
The right triangles in the gate are
45-45-90 triangles, classified by the
measurements of their angles. The
legs of these triangles are
congruent. The hypotenuse is the
length of the legs multiplied by √2.
The right triangle to the right of the
gate is a 30-60-90 right triangle,
also classified by the measure of its
angles. The length of the smallest
side (x) is doubled (2x) to get the
length of the hypotenuse. To find the 18
length of the middle side, it is
multiplied by radical 3, (x √3).

19. Floor Tiles – Tessellation (Investigation 9)
This is a picture of a tiled floor
hallway in my house.
I have left this photograph
fairly untouched because the
lines between the tiles are
fairly distinct. I have, however,
outlined the perimeter of the
hallway lightly in black.
The squares in picture form a
very simple regular
tessellation. Definitions:
A tessellation is a repeating pattern of plane figures that
completely covers a plane with no gaps or overlaps.
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A regular tessellation is the simplest kind of tessellation, a
repeating pattern of congruent regular polygons.

20. Geometry in Nature – Triangular Dog’s Head (L. 51)
This is the head of my greyhound,
Opal.
Her head is shaped like an acute
isosceles triangle, Triangle QRS. <Q
and <R have congruent measures,
while the vertex angle, <S does not.
This is because the angle across from
the line segment that is not
congruent to the other two line
segments will not be congruent to the 20
other two angles of the triangle. In
Triangle QRS, Line Segment QS and
Line Segment RS, the legs, are
congruent, while Line Segment QR is
Definition:
not.
T h e o r e m 5 1- 1:
Is o s c e le s An acute triangle is a triangle with three acute angles (angles with measures less
T r ia n g le than 90°)
T h e o r e m – If a An isosceles triangle is a triangle with at least two congruent sides. 20
t r ia n g le is
A vertex angle is the angle formed by the legs of the triangle.
is o s c e le s , t h e n

21. Geometry in Nature - Starfish
This is a starfish I found on a
trip to the beach last summer. I
then took it home and created
an ornament using a nail and a
piece of string.
A starfish has five legs, each leg
with two sides. This gives it a
total of ten sides, making it a
decagon¹.
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¹ See slide # 4 for a definition of “decagon.”

22. Geometry in Nature – Spherical Plants
This plant is called an Allium, which,
when bloomed, is a sphere of purple
blossoms. My mother plants many
Alliums in her garden at home, and
this is where I found it.
From the plant, you can see the
center from which the blossoms
stems has been labeled as the
center of the sphere (Point A), and
two of the buds have been labeled as
points (Point C and Point B). These
buds represent points on the
sphere’s exterior.
D e f in it io n s :
A s p h e r e is a s e t o f p o in t s in
s p a c e t h a t a r e a f ix e d d is t a n c e
f r o m a g iv e n p o in t c a lle d t h e
c e nte r o f the s p he re . 22

23. Bibliography
• Saxon Geometry. Student ed. Austin: HMH Supplemental Publishers
Inc., 2009. 800-871. Print.
• "circle." Dictionary.com Unabridged. Random House, Inc. 11 Jun.
2012. <Dictionary.com
http://dictionary.reference.com/browse/circle>.
• Simmons, Bruce. "Frustum of a Cone or Pyramid." Mathwords. N.p.,
March 24, 2011. Web. 11 Jun 2012.
<http://www.mathsisfun.com/quadrilaterals.html>.
• "Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid,
Parallelogram." MathIsFun.com. N.p., 2012. Web. 11 Jun 2012.
<http://www.mathsisfun.com/quadrilaterals.html>.
• . "Rectangular Prism - Geometry - Math Dictionary."
icoachmathc.com. High Points Learning Inc, 199-2011. Web. 12 Jun
2012.
<http://www.icoachmath.com/math_dictionary/Rectangular_prism.h
tml>.
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