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Geometry In My World
By: Joshua L
Hexagonal Prism
The picture shown here is of a light in my hallway I use this everyday. This is also a hexagonal prism.
What I Learned:The formula for the lateral area of a prism is L=ph. p= perimeter of base. h= prism’s height.
The formula for the surface area of a prism is S=L+2B. L= lateral area. B= area of base.
The formula for the volume of a prism is V=Bh. B= area of base. h= height of prism.
Skew Lines
The picture here shows an edge of the wall in my house which I see everyday.
What I Learned:These are skew lines because they are not coplanar and don’t intersect. Here, the 2 blue lines are skew lines and the 2 red lines are skew lines. They are both not on the same plane and both don’t intersect. However the blue and the red lines do intersect and are not skew lines.
Cone
Pictured here is my Christmas tree which I use to celebrate the Christmas season. It is also a cone.
What I Learned:The surface area formula for a cone is S = L + B. L = lateral area. B = area of base.
The volume of a cone is V = 1/3Bh. B = area of base. h= length of cones altitude.
The lateral surface area of a cone is L = πrl. r = radius. l = slant height.
Octagon
The picture here is of a light in my house I use it everyday also. It is also in the shape of an octagon.
What I Learned:A central angle of a regular polygon has its vertex at the center of the polygon and its sides pass through consecutive vertices.
Angle A is a central angle.
A
Hemisphere
The picture here is showing a hat. It could also represent a hemisphere.
What I Learned:The surface area of a hemisphere is half of 4 multiplied by pi by the radius squared
S=(4πr ²)/2
Parallel Lines
The picture here is of my dresser where I hold my clothes. It also portrays parallel lines.
What I Learned: According to Postulate 5-7, if 2 lines are parallel to the same line, then they are parallel to one other.
Here the 2 yellow lines are parallel because they are both parallel to the pink line.
Convex Polygon
This is a picture of a window from the inside of my house
What I Learned:
This is a convex polygon because every diagonal is inside it except for the endpoints.
Concave polygons have at least 1 diagonal that goes outside the object.
Major Arc
B
A
C
This is a picture of a carbon monoxide alarm inside my house which detects deadly fumes.
What I Learned:
Major arcs are arcs which are larger than half a circle.
Here arc ABC is the major arc.
Arc AC is a minor arc because it is less than a half circle.
Polyhedra
This is a picture of a fan in my bedroom which helps circulate air in my room.
What I Learned:
A is a face or a lateral face because it is not a base and is a flat surface.
B is an edge because it is the intersection of 2 faces.
C is a vertex because it is an intersection of 3 or more edges.
A B
C
Arc Length
ab
m°
r
c
This is a picture of a C.D., which can play a video game, with rainbow streaks in it which I am using as radiuses.
What I Learned:
To find the length of an arc you use the formula
L= 2πr (m°/360°)
r= radius
m°= degree measure of the arc.
Circumcenter
This is a picture of an award my mother got from her previous job.
What I Learned:
The circumcenter is formed at the intersection of all the perpendicular bisectors.
The circumcenter is equidistant from all the angles of the triangle.
This means all the green segments are the same size.
Cylinder
This is a picture of a rain stick which is in the shape of a cylinder which we use as decoration.
What I Learned:
The lateral area of a cylinder is L= 2πrh
r= radius
h= height of cylinder
The surface area of a cylinder is S= 2πr ²+2πrh
The volume of a cylinder is V= πr²h
Parallelogram
This is a picture of a painting above my computer.
What I Learned:
If an angle in a parallelogram is a right angle, then it is a rectangle.
If the diagonals of a parallelogram are congruent, then it is a rectangle.
Rotation
a
a
This is a picture of a dictionary before and after a rotation
What I Learned:
A rotation is a turn about a point such that each point and its image are the same distance from that point.
The dictionary never changed shape or size, it just turned as if point a was stationary and it fell to the right.
Similarity
This is a picture of a piece of art hung up on a wall in my house.
What I Learned:
Similar polygons have congruent corresponding angles and the corresponding sides are proportional.
This means the corresponding angles are the same degree and the sides have the same ratio.
This is a picture of a lampshade from the side which looks like a trapezoid.
What I Learned:
The bases of a trapezoid are the 2 parallel segments. In this specific example they are on the top and bottom.
The legs of a trapezoid are the 2 nonparallel segments. They are the 2 sides .
Base angles of isosceles trapezoids are congruent and so are the diagonals .
Parts of a Trazpezoid
Tangents
This is a picture of 2 oranges of different sizes.
What I Learned:
A common tangent is tangent to 2 circles.
The tangents here are both internal.
Theorem 58-3 says if 2 tangents are drawn to a circle from the same exterior point, then they are congruent.
Supplementary Angles
ba
The picture here is of a corner of a room.
What I Learned:
When 2 angles add to 180° they are supplementary.
Theorem 6-2 says if 2 angles are supplementary to the same angle or to congruent angles, then they are congruent
Theorem 6-3 says if 2 angles form a linear pair, then they are supplementary.
Trapezoids
b1
b2
This is a picture of one of my sneakers.
What I Learned:
Area of a trapezoid is
A= ½(b1+b2)h
h= height of trapezoid
b1= length of base 1
b2= length of base 2
Circles
This is a picture of the top of a lamp.
What I Learned:
The center of a circle is a point that is a fixed distance from the rest of the circle.
A radius is the measure from the center to the edge of the circle.
The diameter is double the radius and goes through the center to both sides of the circle.
Circumference of a circle is all the way around a circle. It is found by this formula; C= 2πr; r= radius
Area of a circle is A= πr²
