Pythagorean Theorm
Converse of Pythagorean Theorm
DEFINITION: "Let triangle have sides of length a, b, and c. If a2 (squared) + b2 = c2, then the triangle is a right triangle and the angle opposite the side of length c is the right angle." This goes along with the hypotenuse because if the triangle is right then the side across from the 90 angle is the hypotenuse.
Hypotenuse
WHAT IS IT?: The longest side of the triangle, that has to be across from the 90 degree angle.
EQUATION
WHAT DOES THIS MEAN?: "The sum of the areas of squares on the legs of a right triangle is equal to the area of the square on the hypotenuse." Also triangle must be a right triangle.
a2 + b2 = c2
Area
What is area?
WEIRD LOOKING SHAPES: When it comes to nonnormative shapes the best way I see it is cut the shape up into normal shapes like rectangles and triangles to get the area of the whole shape. For finding the area of a circle is a little different then normal because you are using pi (3.14). The equation for a circle is pi X by the radius and then it is squared.
HOW TO FIND AREA?: When finding the area of a shape it all depends on what shape it is. For example for finding the area of a rectangle it is the length X width. For a paraellogram it is the base X height.
REAL LIFE DEFINITION: Area- How much space a shape or object takes up.
BOOK DEFINITION: Area- "The number of units required to cover a region in the plane without overlap..."
Perimeter
What is Perimeter?
HOW TO FIND PERIMETER?: If the shape or object is on a piece of graph paper you can just count the squares around the object and you get the perimeter. But if it is for a circle it is a little different. For a circle one needs to find the circumference of the circle. The equation for the circumference is pi (3.14) X the distance.
REAL LIFE DEFINITION: Perimeter- Is the length around the shape or object.
BOOK DEFINITION: Perimeter- "The length measurement and is given in centimeters, inches, feet, meters and so on."
4 "W"s of Measure
What are they?
hoW?: How will you measure?
WHAT?: What tools will you use?
WHERE?: Our why helps us determine the why. Where are you measuring? Area, perimeter, volume?
WHY?: Why do we measure?
Geometry Unit!
Surface Area
SURFACE AREA OF SHAPES
CIRCLE: One way we were told to solve e for a circle is take pi r squared. First you have to find r, by doing this you take the diameter divided by 2. After you get that you put that answer in for r and solve.
EXAMPLE: The diameter of the circle is 2 3/8 and that divided by 2 is 1 3/16. So pi r squared is 1 3/16 times pi, then squared is 4.43 in squared.
TRIANGLES: Our example in class was taking a whole shape and finding the surface area of the different shapes inside of the whole shape. So the triangle in our whole shapes, we used the pythagorean theorem.
EXAMPLE: 2 3/4 squared + b squared = 5 1/2 squared. So 7.5625 + b squared = 30.25. Then you take 7.5625 away from 7.5625 so now it is b squared= 22.6875 and you take the square root of that number and it equals 4.76.
DEFINITION: How much exposed area a solid object has, also expressed in squared units.
Volume
DEFINTION: The amount of space that a substance or object occupies or an enclosed container can hold.
HOW TO FIND VOLUME?: In a prism or a cylinder it is just base X height. Then for a pryamid or a cone it is one !/3 base X height. It is different from a prism or cylinder because a pyramid and cone have a point or apex on them cutting off some of the shape.
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