The document describes various geometric shapes and concepts that the author observed in her everyday life. It includes 21 examples from her living room, kitchen, and other areas of her house. Each example includes an image, name of the shape or concept, and relevant properties or definitions. The document uses real-world contexts to teach geometry.

1. Geometry in My World
By Megan T
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2. Isosceles Right
Triangle
•This is a picture of the
beams in my living
room. Where they meet
in the corner of the room
creates an isosceles
right triangle.
•Theorem 51-1:
Isosceles Triangle
Theorem- if a triangle is
isosceles, then its base
angles are congruent.
2

3. Line of
Symmetry
•This is a picture of my
living room fireplace. If
you split the fireplace
directly down the middle,
there is a visible line of
symmetry.
•Line of symmetry- a line
that divides a plane figure
into 2 congruent reflected
halves.
3

4. Rectangular
Prism
•This is a picture of a
shoe box. It is a
rectangular prism.
•Prism-a polyhedron
formed by 2 parallel
congruent polygonal
bases connected by
lateral faces that are
parallelograms.
•V = Bh
•S = L + 2B
•L = ph
4

5. Parallel Lines
•This is a picture of the
beams on the ceiling of
my living room. Each
beam is parallel to the
others.
•Parallel lines- lines in the
same plane that don’t
intersect.
•Theorem 5-7: Transitive
Property of Parallel Lines-
if 2 lines are parallel to
the same line, then they
are parallel to one other.
5

6. Cylinder
•This is a picture of many
cylinders piled on each
other. Each cylinder is a
different size.
•Cylinder- a 3-D figure
with 2 parallel congruent
circular bases and a
curved lateral surface that
connects the bases.
•V = Πr2h
•S = 2Πr2 + 2Πrh
•L = 2Πrh
6

7. Vertical
Angles
•This is a picture of a light
in my house. There are 2
lines intersecting that
form vertical angles.
•Vertical angle- the
nonadjacent angles
formed by 2 intersecting
lines.
•Theorem 6-4: Vertical
Angle Theorem- if 2
angles are vertical
angles, then they are
congruent.
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8. Supplementry
Angles
•This is a picture of
drawers in my kitchen.
The angles of each
drawer are
supplementary angles.
•Supplementary angles- 2
angles whose measures
have a sum of 180°.
•Theorem 6-2: Congruent
Supplements Theorem- if
2 angles are
supplementary to the
same angle or to
congruent angles, then
they are congruent
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9. Sphere
•This is a picture of a
soccer ball. A soccer
ball is in the shape of a
sphere.
•Sphere- the set of
points in space that are
a fixed distance from a
given point called the
center of the sphere.
•V = 4/3Πr3
•S = 4Πr2
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10. Trapezoid
•This is a picture of
the corner of the door
frame. The corner is
shaped like a
trapezoid.
•Trapezoid- a
quadrilateral with
exactly one pair of
parallel sides.
•A = ½(b1 + b2)h
10

11. Circle
•This is a picture of a pot
which is in the shape of a
circle.
•Circle- the set of points
in a plane that are a fixed
distance from a given
point called the center of
the circle.
•C = 2Πr or C = Πd
•L = 2Πr(m°/360°)
•A = Πr2
•A(sector) = Πr2(m°/360°)
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12. Perpendicular
Lines
•This is a picture of a
window in my house. The
window panes are
perpendicular lines.
•Perpendicular lines-
lines that intersect at 90°
angles.
•Postulate 19:
perpendicular Lines
Theorem- if 2 non-vertical
lines are perpendicular,
then the product of their
slopes is -1. Vertical and
horizontal lines are
perpendicular to each
other.
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13. Obtuse Angle
•This is a picture of
my ceiling in my
house. It comes
together to form an
obtuse angle.
• obtuse angle- an
angle that measures
greater than 90° and
less than 180°.
13

14. Points On A
Plane
•This is a picture of my
kitchen tablecloth. Each little
square on it represents a
point on a plane which is the
tablecloth as a whole.
•Theorem 4-1: if 2 lines
intersect, then they intersect
at exactly 1 point.
•Theorem 4-2: if there is a
line and a point not on the
line, then exactly one plane
contains them.
•Theorem 4-3: if 2 lines
intersect, then there exists
exactly 1 plane that contains
them.
14

15. Same-Side
Interior Angles
•This is a picture of the
railing of my stairs. The
poles that connect to the
railing create same-side
interior angles.
•Theorem 10-3: Same-
Side Interior Angles
Theorem- if 2 parallel
lines are cut by a
transversal, then the
same-side interior angles
are supplementary.
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16. 45°-45°-90°
Triangle
•This is a picture of a
quilt. On the quilt are
several 45°-45°-90°
triangles.
•Properties of a 45°-45°-
90° Triangle: Side
Lengths- in a 45°-45°-90°
right triangle, both legs
are congruent and the
length of the hypotenuse
is the length of a leg
multiplied by √2.
16

17. Complementary
Angles
•This is a picture of a
window in my house. The
wood on the window
makes complementary
angles.
•Complementary angles-
2 angles whose
measures have a sum of
90°.
•Theorem 6-1: Congruent
Complements Theorem-
if 2 angles are
complementary to the
same angle or to
congruent angles, then
they are congruent.
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18. Concave
Polygon
•This is a picture of a
star decoration. A star
is a concave hexagon.
•Concave polygon- a
polygon in which a
diagonal can be drawn
such that part of the
diagonal contains
points in the exterior of
the polygon.
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19. 30°-60°-90°
Triangle
•This is a picture of one of
my stairs. The stair is a
30°-60°-90° triangle.
•Properties of 30°-60°-90°
Triangles- in a 30°-60°-
90° triangle, the length of
the hypotenuse is twice
the length of the short
leg, and the length of the
longer leg is the length of
the shorter leg times √3.
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20. Skew Lines
•This is a picture of a
tissue box. The tissue
box has skew lines.
•Skew lines- lines that
are not coplanar and
not parallel.
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21. Cone
•This is a picture of a
lamp shade. It is in the
shape of a cone.
•Cone- a 3-D figure
with a circular base
and a curved lateral
surface that connects
the base to a point
called the vertex.
•V = 1/3Bh
•S = Πr2 + Πrl
•L = Πrl
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