Let's review some formulas.
Area and Perimeter
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Area of a circle
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Wednesday, October 10, 2012
We are going to review identification of angles.
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Identify Points and Lines in Geometry
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Classify a Triangle by the angles
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Monday, October 8, 2012
The Pythagorean Theorem.
Today we are going to be learning how to find a side or the hypotenuse of a right triangle by using the Pythagorean Theorem.
Today we are going to be learning how to find a side or the hypotenuse of a right triangle by using the Pythagorean Theorem.
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Pythagorean Theorem
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen.
The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen.
Monday, October 1, 2012
1. What is the diameter of a circle with radius of 7 inches?
2. What is the circumference of a circle with diameter of 5 centimeters?
3. What is the area of a circle with a radius of 3.5 feet?
4. What is the radius of a circle with a diameter of 9 centimeters?
5. If the circumference of a circle is 28.26 inches, then what is its diameter?
6. If the area of a circle is 12.56 square centimeters, then what is its radius?
7. If the diameter of a circle is 3.4 inches, then what is the radius?
8. What is the circumference of a circle if its radius is 4 meters?
9. What is the area of a circle if its diameter is 9 centimeters?
10. The distance around a bicycle wheel is 21.98 feet. What is its diameter?
11. The area of a DVD is 12.56 square centimeters. What is its diameter?
12. The circumference of a dinner plate is 15.7 inches. What is its radius?
13. The area of a CD-ROM is 78.5 cm
14. What is its diameter?
2. What is the circumference of a circle with diameter of 5 centimeters?
3. What is the area of a circle with a radius of 3.5 feet?
4. What is the radius of a circle with a diameter of 9 centimeters?
5. If the circumference of a circle is 28.26 inches, then what is its diameter?
6. If the area of a circle is 12.56 square centimeters, then what is its radius?
7. If the diameter of a circle is 3.4 inches, then what is the radius?
8. What is the circumference of a circle if its radius is 4 meters?
9. What is the area of a circle if its diameter is 9 centimeters?
10. The distance around a bicycle wheel is 21.98 feet. What is its diameter?
11. The area of a DVD is 12.56 square centimeters. What is its diameter?
12. The circumference of a dinner plate is 15.7 inches. What is its radius?
13. The area of a CD-ROM is 78.5 cm
14. What is its diameter?
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Classification of Circles
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What is the sum of angles in various shapes?
Class assignment
Volume and Surface Area
The side of a cube measures 3. What will be the volume and surface area of the cube?
The length of a cuboid is 4, width is 5 and height is 12. What is its volume and surafce area?
Surface Area of a cube is 294 m2. Calculate its side.
The surface area of a cuboid is 112.Its length is 4 and height is 8. Find its breadth.
Radius of a sphere is 8. What is its volume?
Radius of a sphere is 2. What is its volume and surface area?
Volume of a sphere is 16. What is its radius?
A cube has a side of 16 cm. Another cube has a side of 4 cm. Tell the number of smaller cubes that will fit into larger cube.
It costs $5 to paint 1m2 of area. How much would it cost to paint a room with length 3.5m, breadth 4 m and height 5 m (both inside and outside the room)?
It costs 1 unit paint to paint 1 box of a rubix cube. How much paint would it cost to paint all the boxes of the rubix cube?
The length of a cuboid is 4, width is 5 and height is 12. What is its volume and surafce area?
Surface Area of a cube is 294 m2. Calculate its side.
The surface area of a cuboid is 112.Its length is 4 and height is 8. Find its breadth.
Radius of a sphere is 8. What is its volume?
Radius of a sphere is 2. What is its volume and surface area?
Volume of a sphere is 16. What is its radius?
A cube has a side of 16 cm. Another cube has a side of 4 cm. Tell the number of smaller cubes that will fit into larger cube.
It costs $5 to paint 1m2 of area. How much would it cost to paint a room with length 3.5m, breadth 4 m and height 5 m (both inside and outside the room)?
It costs 1 unit paint to paint 1 box of a rubix cube. How much paint would it cost to paint all the boxes of the rubix cube?
Answers to above
Volume: 27 and Surface Area: 54
Volume: 240 and Surface Area: 256
Side: 7
Breadth: 2
Volume: 2143.57
Volume: 33.49 and Surface Area: 50.24
Radius: 1.563
Answer: 64
Answer: $515
Answer: 54 unit paint
Volume: 240 and Surface Area: 256
Side: 7
Breadth: 2
Volume: 2143.57
Volume: 33.49 and Surface Area: 50.24
Radius: 1.563
Answer: 64
Answer: $515
Answer: 54 unit paint
Angles
Find the measure of an angle that is complementary to:
Use the diagram next to this question for exercises 8-9. Note that NK is perpendicular to IK 5. Name two complimentary angles. 6. If the measure of angle INJ is 63 degrees, what is the measure of angle KNJ. 7. Complementary angles add up to 8. Supplementary angles add up to 9. A figure bound by three lines is a 10. The smallest angle of a triangle is opposite the smallest/largest side? |
Definitions:
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Monday, September 24, 2012
Today we are going to be learning more about angles.
Two angles are complementary if the sum of their angles equals 90 degrees.
If one angle is known, its complementary angle can be found by subtracting the measure of its angle from 90 degrees.
Example: What is the complementary angle of 43 degrees?
Solution: 90 degrees - 43 degrees = 47 degrees
Two angles are supplementary if the sum of their angles equals 180 degrees.
If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180 degrees.
Example: What is the supplementary angle of 143 degrees?
Solution: 180 degrees - 143 degrees = 37 degrees
Two angles are complementary if the sum of their angles equals 90 degrees.
If one angle is known, its complementary angle can be found by subtracting the measure of its angle from 90 degrees.
Example: What is the complementary angle of 43 degrees?
Solution: 90 degrees - 43 degrees = 47 degrees
Two angles are supplementary if the sum of their angles equals 180 degrees.
If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180 degrees.
Example: What is the supplementary angle of 143 degrees?
Solution: 180 degrees - 143 degrees = 37 degrees
Angle
A geometric figure formed by two rays with a common endpoint.
Acute Angle
An angle that is greater than 0 degrees and smaller than 90 degrees.
Adjacent Angles
Two angles that have a common vertex and a common ray.
Congruent Angles
Angles that have the same measure.
Vertical Angles
Angles that are formed by intersecting lines.
These are angles that are opposite of each other. Obtuse Angle
An angle that is greater than 90 degrees and less than 180 degrees.
Vertex
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Complimentary Angles
A pair of angles whose measures have a sum of 90 degrees are complementary angles. If these angles are adjacent, they will form a right angle.
Two angles are complementary if the sum of their angles equals 90 degrees. If one angle is known, its complementary angle can be found by subtracting the measure of its angle from 90 degrees. Example: What is the complementary angle of 43o? Solution: 90 degrees - 43 degrees = 47 degrees Supplementary Angles
A pair of angles whose measures have a sum of 180 degrees are supplementary angles. If these angles are adjacent, they will form a straight angle.
Two angles are supplementary if the sum of their angles equals 180 degrees. If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180 degrees. Example: What is the supplementary angle of 143 degrees? Solution: 180 degrees - 143 degrees = 37 degrees |
Identifying Triangles
There are seven types of triangle, listed below. Note that a given triangle can be more than one type at the same time. For example, a scalene triangle (no sides the same length) can have one interior angle 90°, making it also a right triangle. This would be called a "right scalene triangle".
Isosceles Triangle
The word isosceles is pronounced "eye-sos-ell-ease" with the emphasis on the 'sos'. It is any triangle that has two sides the same length.
A triangle which has two of its sides equal in length. Scalene Triangle
Greek: skalenos - "uneven, unequal"
A triangle where all three sides are different in length. Sometimes called an irregular triangle. Scalene triangles are triangles where each side is a different length. They are unusual in that the are defined by what they are not. Most triangles drawn at random would be scalene. The interior angles of a scalene triangle are always all different. The converse of this is also true - If all three angles are different, then the triangle is scalene, and all the sides are different lengths. Right Triangle
Right - upright or 'perfect'
A triangle where one of its interior angles is a right angle (90 degrees). Right triangles figure prominently in various branches of mathematics. For example, trigonometry concerns itself almost exclusively with the properties of right triangles, and the famous Pythagoras Theorem defines the relationship between the three sides of a right triangle: a2 + b2 = h2 where h is the length of the hypotenuse a,b are the lengths of the the other two sides Obtuse Triangle
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Equilateral Triangle
Latin: aequus -"equal" , latus -"side"
A triangle which has all three of its sides equal in length. An equilateral triangle is one in which all three sides are congruent (same length). Because it also has the property that all three interior angles are equal, it really the same thing as an equiangular triangle. Equiangular Triangle An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60°
The sides of an equiangular triangle are all the same length (congruent), and so an equiangular triangle is really the same thing as an equilateral triangle. Acute Triangle
From Latin: acutus - "sharp, pointed"
A triangle where all three internal angles are acute (less than 90 degrees). Hypotenuse
From Greek "to stretch"
The longest side of a right triangle. The side opposite the right angle. |
Monday, September 17, 2012
We are going to learn about basic geometric figures and their relationships among points, segments, and lines.
There are some basic geometric concepts to know. Please write the following terms in your geometry journal.
There are some basic geometric concepts to know. Please write the following terms in your geometry journal.
PlaneA flat surface that extends endlessly in all directions.
TheoremA statement that can be proven.
LineA geometric figure that extends endlessly in two directions.
BisectorA line that intersects a line segment at its midpoint.
Line SegmentA part of a line that has two end points.
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RayA part of a line with one endpoint.
Collinear PointsPoints on the same line.
Congruent Line SegmentsLine segments that have the same length.
MidpointThe point that divides a line segment into two congruent parts.
PointA location in space
PostulateA statement that is accepted without proof.
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Area and Perimeter of Triangles
Today we are going to learn about finding the area and the perimeter of triangles.
How to find the area of a triangle:
How to find the perimeter of a triangleWe find the perimeter the same way we did with squares and rectangles: by adding the sides.
Question:For an art project, a pentagon made of construction paper is cut into five equal slices. Two of the slices are removed. Write the remaining portion of the pentagon as a fraction.
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Types of triangles based on their angles
Types of triangles based on their sides
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Monday, September 10, 2012
Area of Squares and RectanglesToday we are going to learn about how to find the area of squares and rectangles. There are two ways of doing this. One way that we can do this is to count the number of units. Another way of doing this is by using a formula. Feel free to pause at any time when you feel you need to repeat the information.
What is Perimeter?The distance AROUND the shape. In today's example, we will be working with squares and rectangles.
What is Area?The area is the number of square units needed to cover the surface.
What is a Square?A square is a parallelogram, or a four sided figure, that has four right angles and four sides of the same length. When the four sides are the same length, we can say that these sides are congruent.
What is a Rectangle?A rectangle is a four sided figure with right angles just like a square. The difference is that the opposite sides are congruent, or even.
Calculating the Perimeter of a Square
The perimeter of a square is the distance around the outside of the square. A square has four sides of equal length. The formula for finding the perimeter of a square is 4*(Length of a Side).
Calculating the Perimeter of a Rectangle
The perimeter of a rectangle is the distance around the outside of the rectangle. A rectangle has four sides with opposite sides being congruent. The formula for finding the perimeter is:
Side A + Side B + Side A + Side B. This could also be stated as: 2 x Side A + 2 x Side B or 2 x (Side A + Side B) Calculating the Perimeter of a Parallelogram
The perimeter of a parallelogram is the distance around the outside of the parallelogram. A parallelogram has four sides with opposite sides being congruent. The formula for finding the perimeter is Side A + Side B + Side A + Side B. This could also be stated as:
2 x Side A + 2 x Side B or 2 x (Side A + Side B). |
Learn more about perimeter and area of regular shapes. A common mistake is to confuse the perimeter which is the distance around an object with area which is the square units within the object. Activity:Take various measurements of some common items.
Find the area and perimeter of these items. Measure the perimeter of your table top. Now find the area of that table top. How to find the area of a parallelogram:
How to find the area of a square
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