Aim: How do we use scant, chord and tangent ratios in cirles?
-If Two cords intersect inside a circle, then the prodect of the segements of one cord equals the product of the segements of the other chord.
-Theorem 84: If two secant segements intersect outside a circle, then the product of the secant segements with its external portion.
WO=WO
Sunday, May 6, 2012
How do you find the surface area and volume of a sphere?
Aim: How do you find the surface area and volume of a sphere?
SPHERES
- A sphere is the set of all points in the space equidistant from given point called the center.
Formulas:
SA= 4(3.14r^2)
LA= 4(3.14r^2)
For Example:
1. find the Surface area of the Sphere
r=17
formula=4(3.14r^2)
Step 1: write the formula if you want
EX: formula=4(3.14r^2)Step 2: Plug in the given information into the formula
EX: SA=4(3.14r^2) R=17
SA:4(3.14*17^2)
Step 3: Solve the problems
EX: 4(3.14x17^2)
4(3.14x289)
4(907.9)
SA=3631.6
Try on your own:
Solve for SA
R=13
SPHERES
- A sphere is the set of all points in the space equidistant from given point called the center.
Formulas:
SA= 4(3.14r^2)
LA= 4(3.14r^2)
For Example:
1. find the Surface area of the Sphere
r=17
formula=4(3.14r^2)
Step 1: write the formula if you want
EX: formula=4(3.14r^2)Step 2: Plug in the given information into the formula
EX: SA=4(3.14r^2) R=17
SA:4(3.14*17^2)
Step 3: Solve the problems
EX: 4(3.14x17^2)
4(3.14x289)
4(907.9)
SA=3631.6
Try on your own:
Solve for SA
R=13
How do we find the surface area and lateral area of pyramids and cones?
Aim: How do we find surface area and lateral area of pyramids and cones?
Do Now: Reviewing Triangles
1. Find the area of the triangle
height is 20 and the base is 16
Pyramid
A pyramid is a solid that connect a polygon base to point. The Pyramid has 3 triangle faces and a base that is a square.
The Slant Height of a pyramid is the height of one of the lateral faces.
* Formulas*
Lateral area= (1/2)pl
SA= L.A+B
Solve for lateral area and surface area
Do Now: Reviewing Triangles
1. Find the area of the triangle
height is 20 and the base is 16
Pyramid
A pyramid is a solid that connect a polygon base to point. The Pyramid has 3 triangle faces and a base that is a square.
The Slant Height of a pyramid is the height of one of the lateral faces.
* Formulas*
Lateral area= (1/2)pl
SA= L.A+B
Solve for lateral area and surface area
Saturday, May 5, 2012
How do we find the area of parallelograms, kites and trapezoids?
Aim: How do we find the area of parallelograms, kites and trapezoids?
Area of a Trapezoid is the 1st base + the 2nd base and then you divide by 2 and then times the height given in the trapezoid.
Formula: b1+b2/2*H
Try it out:
1. Base 1=14
Base 2=12
The Height=6
Area of a Kite is the first diagonal times the 2nd diagonol divided by 2.
Formula: d1*d2/2
Try it:
1. Diagonal 1=7
Diagonal 2= 16
Area of a Trapezoid is the 1st base + the 2nd base and then you divide by 2 and then times the height given in the trapezoid.
Formula: b1+b2/2*H
Try it out:
1. Base 1=14
Base 2=12
The Height=6
Area of a Kite is the first diagonal times the 2nd diagonol divided by 2.
Formula: d1*d2/2
Try it:
1. Diagonal 1=7
Diagonal 2= 16
How do we calculate the area of rectangles and triangles ?
Aim: How do we calculate the area of rectangles and triangles ?
Triangle Area Conjecture= (1/2)bh
The Area of a triangle is given by the formula A=(1/2)bh. A is the Area, B is the length of the base, and H is the height of the triangle.
Example:
The Triangle ABC.
The Length of AC is 9mm and the length of AB is 20mm.
Step1: Know the given information, The problem gave you already that the length of the base is 9mm and also that the height is 20mm.
Step2: plug the new information in the formula A=(1/2)bh
Ex: A=(1/2) 9 X 20
Step 3: Multiply The base and the height
Ex: 9 X 20= 180
Step4: Once you got your answer divide the answer by 2
180/2= 90
And the answer to the problem above is 90mm^2
Triangle Area Conjecture= (1/2)bh
The Area of a triangle is given by the formula A=(1/2)bh. A is the Area, B is the length of the base, and H is the height of the triangle.
Example:
The Length of AC is 9mm and the length of AB is 20mm.
Step1: Know the given information, The problem gave you already that the length of the base is 9mm and also that the height is 20mm.
Step2: plug the new information in the formula A=(1/2)bh
Ex: A=(1/2) 9 X 20
Step 3: Multiply The base and the height
Ex: 9 X 20= 180
Step4: Once you got your answer divide the answer by 2
180/2= 90
And the answer to the problem above is 90mm^2
Sunday, April 22, 2012
The Elegant Locus
Aim: The Elegant Locus
Definition: The locus is the set of all points that satisfy a given condition.
- A locus is a general graph of given equation.
- The locus of points equidistant from a single point is set of point, equidistant from the point, in every direction.
- The locus of points equidistant from a single point is a set of points, equidistant from the point, in every direction.
- The Locus of points equidistant from two points is perpendicular bisector of the line segment connecting the two points.
- The locus of points equidistant from a line are two lines, on opposite sides, equidistant and parallel to that line.
- The locus of points equidistant from two parallel lines is another line, half way between both lines, and parallel to each of them.
-The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles fromed by the original lines.
Try now: From Regentsprep.org
Definition: The locus is the set of all points that satisfy a given condition.
- A locus is a general graph of given equation.
- The locus of points equidistant from a single point is set of point, equidistant from the point, in every direction.
- The locus of points equidistant from a single point is a set of points, equidistant from the point, in every direction.
- The Locus of points equidistant from two points is perpendicular bisector of the line segment connecting the two points.
- The locus of points equidistant from a line are two lines, on opposite sides, equidistant and parallel to that line.
- The locus of points equidistant from two parallel lines is another line, half way between both lines, and parallel to each of them.
-The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles fromed by the original lines.
Try now: From Regentsprep.org
The locus of points equidistant from two intersecting lines is ...
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Choose:
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Sunday, April 15, 2012
Aim: How do we identify solids ?
Aim: How do we identify solids ?
Cross sections: The shape you get when you cut straight down
Surface Area: The area of the bases + the Lateral Area ( area of the side)
Solid Geometry: Solid geometry is the geometry of 3-dimensional space.
Properties:
- Volume
- Surface Area
Two Main types of solid:
- Polyhedra
- Non-Polyhedra
Polyhedra: Flat Surface
- Prism
- Pyramids
- Platonic solids
- Sphere
- Torus
- Cylinder
- Cone
Cross sections: The shape you get when you cut straight down
Surface Area: The area of the bases + the Lateral Area ( area of the side)
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