Geometry/Measurement Project

Corresponding Angles- Two angle sums that add up to 90°

Supplementary Angles- Two angle sums that add up to 180°

Congruent Angles- These are two angles that have the same measure

Angle Measure- the number of degrees of turn to rotate about the vertex

Corresponding Angles- When two lines are crossed by another line, the angles in matching corners are called corresponding angles.

Classification of Angles-

Right Angle- two line segments that have an angle of 90°

Obtuse Angle- Two line segments that have an angle greater than 90°

Acute Angle- Two line segments that have an angle less then 90°

Straight Angle- a line segment that equals 180°

Sum Of Angles For A Triangle- All three angles should add up to 180°.

Polygon- Is a simple closed polygonal curve.

Triangle

Acute Triangle- all three interior angles are acute (the angles have to be less than 90°)

Right Triangle- if one angle is a right angle ( the angle equals 90°)

Obtuse Triangle-If an interior angle is obtuse (if the angle is greater than 90°)

Scalene- No two sides of the triangle have the same length

Isosceles- At least two sides of the triangle have the same length sides

Equilateral- All three sides have to be the same length

Quadrilaterals is any shape that has 4 sides

A kite has two pairs of adjacent congruent sides

A trapezoid has two parallel sides

Isosceles Trapezoid has two sides parallel and two congruent angles

A parallelogram has two pairs of opposite parallel sides

A rhombus is a parallelogram with all the sides of the same length.

A rectangle is a parallelogram with all right angles.

A square has all the sides are the same length and all right angles.

Circle- This shape is different because it does not have any sides.

A regulare polygon is a convex polygon that is both equilateral and equiangular

Alternative Interior Angles- (<f and <d) also (<e and <c )

Alternate Exterior Angles- (<b and <h) also (<a and <g)

Corresponding Angles- (<b and <f) also (<a and <e) also (<d and <h) also (<c and <g)

Polyhedron: a three-dimensional figure made up of sides called faces, each face being a polygon

To determine the volume of a polyhedron, follow the steps below:
1. center the polyhedron at the orgin of the 3-dimensional rectangular coordinate system
2. draw lines from each vertex (corner) to the orgin. Each face is now the base of a pyramid with the orgin as its apex.
3. Calculate the volume of each pyramid. Using pyramids volume formula ( V=(1/3)B*h where B is the area of the base.
4. Add together the volumes of all the pyramids to get the entire volume of the polyhedron.

Circumference is the name of the perimeter of a circle. The equation is C= 2*pi*r where r is the radius. This also means that C=2pi*r

A prism has 2 congruent faces (the bases) in parallel planes and other faces (lateral faces) bounded by parallelograms

Subtopic

The right prism has two lateral faces that are perpendicular to the bases.

An oblique prism has lateral faces that are NOT perpendicular to the faces.

You can easily tell the shape of a prism by its name. For example a triangle right prism has 2 triangle bases meaning there are three sides that have a right angle. A hexagonal oblique prism will be tilted and not have any right angles at all because it is hexagonal we know that it has 6 sides.

Surface area is the sum of the lateral surface areas and the area of the bases

Equations

Cube

6(eXe)

, for a cube with side lengths of 5, you would solve it like so 6(5X5), 6(25), The surface area is 150 Units^2

Prism

PH+2B

This equation takes a lot of explaining, for example P=the perimeter of the base, H=the height of the prism, and B=the AREA of the base

An example would be, P=12, H=10, and B=6. The equation would then be (12X10)+(6X2)- resulting in an answer of 132Units^2

Cylinder

PH+2B

This equation is similar to the prism, only the area of the base would be circular, therefore the "2b" become "2piR^2" and the "PH" becomes "2piRXH"

A cylinder with Radius 2 and Height 4 would be, 2pi(2^2)+ 2pi2X4, 8pi+16pi, or 24pi (Units^2)

Pyramid

B+1/2ps

In this equation B=the area of the base, p=number of sides and s=slant height

For example a pyramid with four sides, a slant height of 3, and a base area of 12 would be, 12+1/2(3X4), 12+6, 18Units^2

Cone

piR^2+piRXs

In this equation S=slant height and R=Radius of the base

A cone with a slant height of 4, and a radius of 6 would be pi6^2+pi6X4, 36pi+24pi=60piUnits^2

Sphere

4piR^2

When radius =3, 4pi(3^2), 4pi(9), 36piUnits^2

You can always just add up the area of all the sides, but there are some equations and tricks to avoiding the hassle and uncertainty of that!

The equation for the Pythagorean Theorem is a^2+b^2=c^2

It is important to remember "C" is always the hypotenuse of the triangle

In this example lets say A=3 B=4 and C is unknown

You would solve "C" by using the equation, 3^2+4^2=C^2, you would then get 9+16=C^2, 25=C^2, C=5 units

The pythagorean theorem only works for right triangles, therefore you can determine if triangle is right by plugging the numbers into the equation

Lets say A=2 B=5 and C=10

2^2+5^2 = 10^2, 4+25=100, or 29=100. This is incorrect, therefore you have identified that this triangle is not a right triangle.

Area is the surface size of a figure. Area is always expressed in units squared.