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Welcome to Ms. D's Geometry Site
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Find all the measurements of the 30-60-90 triangle and use them to calculate perimeter and area of the figure. You can print the attached worksheet to follow along with the videos.
Find the missing measurements of the 30-60-90 triangle. Write your...
Find the missing measurements of the 30-60-90 triangle. Write your answers in simplest radical form.
Find the missing measurements of the 30-60-90 triangle. Write your...
Find the missing measurements of the 30-60-90 triangle. Write your answers as radicals in simplest form.
Use the special right triangle (30-60-90) properties to find the area...
Use the special right triangle (30-60-90) properties to find the area of a triangle. Keep the answer in simplest radical form.
Find the missing measurements of a 30-60-90 triangle. Keep your...
Find the missing measurements of a 30-60-90 triangle. Keep your answers in simplest radical form.
Calculate the length of the hypotenuse of a right triangle using the...
Calculate the length of the hypotenuse of a right triangle using the properties of a 30-60-90 special right triangle.
Calculate the area of a triangle using the properties of a 30-60-90...
Calculate the area of a triangle using the properties of a 30-60-90 special right triangle.
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Use the Special Right Triangle Theorem (45-45-90) to solve for missing side lengths. Apply the theorem to solve for area and perimeter of triangles, squares, and composite figures.
Print the attached worksheet to follow along.
Compare Special Right Triangle Theorem (45-45-90) with the...
Compare Special Right Triangle Theorem (45-45-90) with the Pythagorean Theorem. This example shows you that both methods will yield the same result.
Use Special Right Triangle (45-45-90) to solve for a missing length.
Use Special Right Triangle (45-45-90) to solve for a missing length.
Use Special Right Triangle (45-45-90) to find the missing length.
Use Special Right Triangle (45-45-90) to find the missing length.
Find the area of a square with only the diagonal given. Use special...
Find the area of a square with only the diagonal given. Use special right triangle theorem (45-45-90) to find the missing side length and solve for the area.
Use the special right triangle theorem (45-45-90) to find the area of...
Use the special right triangle theorem (45-45-90) to find the area of a composite shape made up of a square and a semicircle.
Use the special right triangle theorem (45-45-90) to find the...
Use the special right triangle theorem (45-45-90) to find the perimeter of a composite figure made up of a square and a semicircle -- all you have is the length of the diagonal.
Use the special right triangle theorem (45-45-90) to find the missing...
Use the special right triangle theorem (45-45-90) to find the missing side.
Use the special right triangle theorem (45-45-90) to find the missing...
Use the special right triangle theorem (45-45-90) to find the missing length.
Use the special right triangle theorem (45-45-90) to find the area of...
Use the special right triangle theorem (45-45-90) to find the area of a triangle.
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The area of a polygon is the number of square units that the figure covers. Area is measured in square units, such as square feet or square miles. An example is the area of a square whose sides each measure 2 inches long -- the area is 2*2=4 square inches.
Area of a Rectangle
The area of a rectangle is the product of its length and width: A = lw
Area of a Triangle
The area of a triangle is half the area of a rectangle -- half the product of a base and its corresponding height: A = (1/2) bh
Area of a Parallelogram
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel to each other. Any side of a parallelogram can be called a base. Each base has a corresponding altitude, and the length of the altitude is the height of the parallelogram.
The area of a parallelogram is equal to the area of a rectangle with the same base and height as the parallelogram -- the area of a parallelogram is the product of a base and its corresponding height: A = bh
Area of a Regular Polygon
In a regular polygon, all sides are congruent and all angles are congruent. You can find the area of the regular polygon if you know the length of one side of the polygon and the length of the apothem. The apothem is the perpendicular segment from the center of a regular polygon to one of its sides -- the length of the apothem is the height of the triangle formed by a side and the two segments from the center to the endpoints of this side. The area of a regular polygon is half the product of the apothem (a) and the perimeter (P): A = (1/2) a*P
Another way to look at the formula for area of a regular polygon is to find the area of
one the triangles found in the polygon and multiplying by the number of sides in the polygon: A = (1/2) bh * n, where h is the height of the triangle (the apothem of the polygon), b is the length of one side of the polygon and n is the number of sides of the polygon.
This video shows you how to find the area of a regular hexagon if...
This video shows you how to find the area of a regular hexagon if you're given a radical in the side length.
Area of a Quadrilateral with Perpendicular Diagonals
To find the area of a quadrilateral that has perpendicular diagonals (such as rhombus, square, and kite), find the half the product of the diagonals: A = (1/2) d1*d2
 
Area of a Trapezoid
The area of a trapezoid is half the product of the height and the sum of the bases: A = (1/2) h*(b1 + b1)
This video shows you how to find the area of a circumscribed...
This video shows you how to find the area of a circumscribed trapezoid.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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Relationships Between Lines and Planes
 When two lines lie in the same plane and do not intersect, they are parallel to each other.
Two lines that intersect each other and form 90 degree angles are perpendicular to each other.
Lines that do not lie in the same plane and do not intersect are skew lines.
Similarly, if two planes do not intersect each other, they are parallel planes. In the diagram, the top and bottom of the cube represent parallel planes.
Angle Relationships
A line that intersects two or more other lines in a plane is called a transversal. Two lines and a transversal form eight angles. Some pairs of the angles have special relationships.
Corresponding Angles
When two lines are intersected by a transversal, a pair of angles that lie on the same side of the transversal and on the same sides of the other two lines are called corresponding angles. If the lines are parallel, then the corresponding angles are congruent.
In this diagram, angles 4 and 8 are corresponding angles.
 Alternate Interior Angles
When two lines are intersected by a transversal, a pair of nonadjacent angles that lie on opposite sides of the transversal and between the other two lines are called alternate interior angles. If the lines are parallel, then the alternate interior angles are congruent.
In this diagram, angles 4 and 5 are alternate interior angles.
 Alternate Exterior Angles
When two lines are intersected by a transversal, a pair of angles that line on opposite sides of the transversal and outside the other two lines are called alternate exterior angles. If the lines are parallel, then the alternate exterior angles are congruent.
In this diagram, angles 2 and 7 are alternate exterior angles.
 Same-Side Interior Angles
When two lines are intersected by a transversal, a pair of angles that lie on the same side of the transversal and between the two lines are called same-side interior angles. If the lines are parallel, then the angles are supplementary.
In this diagram, angles 4 and 6 are same-side interior angles.
Find the measure of each angle formed by parallel lines and a...
Find the measure of each angle formed by parallel lines and a transversal. Use angle relationships to create algebraic equations.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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If two lines in a plane are cut by a transversal and certain conditions are met, then the lines must be parallel:
- corresponding angles are congruent
- alternate exterior angles are congruent
- consecutive interior angles are supplementary
- alternate interior angles are congruent
- two lines are perpendicular to the same line
You can prove that lines are parallel by using postulates and theorems about pairs of angles. You can also use slopes of lines to prove that two lines are parallel or perpendicular.
 Converse of the Corresponding Angles Postulate
If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
The Converse of the Corresponding Angles Postulate is used to construct parallel lines.
The Parallel Postulate guarantees that for any line m, you can always construct a parallel line through a point that is not on line m.
 Converse of the Alternate Interior Angles Theorem
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.
Converse of the Alternate Exterior Angles Theorem
If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
Converse of the Same-Side Interior Angles Theorem
If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.
Write Equations of Lines
A linear relationship between two variables can be represented by an equation in point-slope form or slope-intercept form. The equation can then be used to analyze the relationship.
You can write an equation of a line if you are given any of the following:
- the slope and the y-intercept
- the slope and the coordinates of a point on the line
- the coordinates of two points on the line
If m is the slope of the line, b is its y-intercept, and (x1, y1) is a point on the line, then:
- the slope-intercept form of the equation is y = mx + b
- the point-slope form of the equation is y - y1 = m(x - x1)
Parallel Lines Theorem
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
Perpendicular Lines Theorem
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1 (they are opposite reciprocals of each other). Vertical and horizontal lines are perpendicular.
This video demonstrates how to write the equation of a line, a line...
This video demonstrates how to write the equation of a line, a line parallel to the original, and a line perpendicular to the original.
Classifying Pairs of Lines
In a system of equations that represents two lines, you need to determine whether the lines are parallel, intersect, or coincide. Lines that are parallel have the same slope, but different y-intercepts. Lines that have different slopes, will intersect each other. Lines that coincide are the same line, but their equations may be written in different forms. In order to determine which classification applies, you need to solve both equations for y to find the slope-intercept form: y = mx + b.
Determine whether the lines are parallel, intersect, or coincide. ...
Determine whether the lines are parallel, intersect, or coincide. Solve both equations for y to find the slope-intercept form of the equations. Compare the slopes and y-intercepts.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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 Three-dimensional figures can be made up of flat or curved surfaces. Prisms and pyramids are named by the shapes of their bases.
A flat surface is called a face. An edge is the intersection of two faces. A vertex is the intersection of three or more faces.
 A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure.
The net at the right has one rectangular face. The remaining faces are triangles. The net forms a rectangular pyramid.
 A cross-section is the intersection of a three-dimensional figure and a plane.
Since the figure on the left is a rectangular pyramid, the cross section is a rectangle.
 An isometric drawing is drawn on isometric dot paper and shows three sides of a figure from a corner view. A solid and an isometric drawing of the solid are shown in the image on the right.
Orthographic views show three-dimensional objects from six different perspectives.
 Top: Picture yourself above the figure and looking straight down.
Front: Choose one side of the figure to be the front. Visualize looking straight at the figure.
Right: Picture walking around to the right side of the figure and looking straight at it.
Bottom: Picture yourself directly underneath the figure and looking straight up.
Left: Picture walking around the corner to the left side of the figure and looking straight at it.
Back: Picture walking around to the back of the figure and looking straight at it.
Perspective Drawings
 A perspective drawing shows parallel lines drawn such that they meet at a vanishing point. In a one-point perspective drawing, nonvertical lines are drawn so that they meet at a vanishing point.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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Remember to practice setting up your trig ratios for our upcoming test. Don't forget to review the videos. Here's one to make you feel better:
This last minute video is designed to make you feel a little bit...
This last minute video is designed to make you feel a little bit better about the upcoming Trig Test
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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Here are two sample problems:
This video shows you how to find the area of a regular hexagon if...
This video shows you how to find the area of a regular hexagon if you're given a radical in the side length.
This video shows you how to find the area of a circumscribed...
This video shows you how to find the area of a circumscribed trapezoid.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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Here are the notes from today's class:
Sector of a circle is the region of a circle bounded by a central angle and its intercepted arc
Segment of a circle is a region of a circle bounded by a chord and its arc.
The area of a segment can be found by subtracting the area of the triangle from the area of the sector (see example below).
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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The Geometry CBA exam will include material that we have covered up to this point -- especially Chapters 6 (Polygons, Quadrilaterals, Parallelograms), 7 (Similarity), and 8 (Right Triangles, Trigonometry, Geometric Mean).
I have attached a short review (pdf). Print the document so that you can follow along with the videos.
This is an introduction to the Geometry Midterm Exam Review (aka...
This is an introduction to the Geometry Midterm Exam Review (aka CBA 3).
We continue our review for the Geometry semester exam (aka CBA) in...
We continue our review for the Geometry semester exam (aka CBA) in part 2 of our series. This video reviews Angle of Depression (Trigonometry)
This video reviews properties of a parallelogram, angles of a kite,...
This video reviews properties of a parallelogram, angles of a kite, and midsegment of a trapezoid.
This video reviews geometric mean, area of a square using the...
This video reviews geometric mean, area of a square using the properties of the diagonals in a parallelogram,
This last part of our semester exam (aka CBA) review demonstrates...
This last part of our semester exam (aka CBA) review demonstrates trigonometric ratios and special right triangles.
Visit www.msdgeometry.com - your ultimate internet resource for comprehensive information on High School Geometry, Algebra, and Trigonometry.
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Dear Students, Parents and/or Guardians,
Welcome back to another exciting year! I am looking forward to a wonderful school year with you. I have provided a brief outline of how my class will be conducted.
During our time together, we will study many concepts such as congruence and similarity, apply properties of lines, triangles, polygons, and circles, and develop reasoning skills. We will also use length, perimeter, area, circumference, surface area, and volume to develop problem solving skills.
In order to be successful, it is important that you maintain a well-organized notebook, complete all assignments, and show all work. Binders will be divided into the following sections: Reference, Daily, HW, Quizzes/Tests, and Progress Reports. To maintain communication with parents and students, I will be sending home progress reports to be signed every 3 weeks. These will be kept in the binder so that we can set goals and monitor achievements.
Rules
· Be in your assigned seat and working on the assignment when the tardy bell rings.
· Bring ALL books and materials to class and take them with you when you leave.
· Treat each person in this room with respect and dignity.
· Do not interfere with teaching or learning.
· Please take care of all restroom needs prior to class.
· Do not bring foods or drinks to class.
· Please remember that the bell does not dismiss you; I dismiss you.
Electronic Devices
In order for you to do your best in this class, we must eliminate unnecessary distractions. You should have your cell phone turned off (not on vibrate). All other devices should also be off and out of sight. If your cell phone is taken up and sent to the office, it will cost $15 to get it back. Other electronic devices will be kept until the end of the day. Parents will be contacted if you frequently offend this rule.
Academic Integrity
Honesty and integrity are expected. These apply to all assignments and include fraud, deception, talking, signs, gestures, copying or any other method of giving or receiving information during a test, quiz or class assignment. A student engaged in academic dishonesty will receive a zero for the assignment being worked on. If one student is copying from another, then both students will be given a grade of zero. If a student wants to discuss the situation, they may quietly discuss the event during conference period, before school or after school.
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FREE DELIVERY on in-stock orders over $79 at Discount School Supply.
You will need the following supplies:
· Three-ring binder (hard cover) with 5 dividers
· Loose-leaf/filler paper (college rule – 150 sheets)
· 3-hole punched graph paper
· Pencils, red grading pen, highlighter, ruler
· 1 box tissues
· Composition notebook (hard cover)
Additional information will be provided on the first day of school.
SmileMakers: Reward, Motivate, Educate
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