[pic]
A parallelogram is a quadrilateral in which pairs of opposite sides are parallel and are congruent. Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same) NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Name the kind of parallelogram this figure displays? Example 1: [pic]
[pic] A parallelogram with:   all sides equal and   angles "a" and "b" as right angles   Is a square! 
Perimeter and area of a parallelogram
Perimeter of a parallelogram:
The perimeter can be calculated with the following formula:
[pic]
Where a and b are the side lengths.
Area of a parallelogram
The area can be calculated with the following formulas:
[pic]
Where b is the length of the base line, and h is the height of the parallelogram.
[pic]
Where a and b are the side lengths and θ is the angle.
[pic]
Example 2: Find the area and perimeter with the given length and side. a: [pic] Side length a 
b: [pic] Side length b 
h: [pic] Height 
θ: [pic] Angle in degrees 
The perimeter is calculated:
[pic]
The area is calculated, using height and b:
[pic]
The area is calculated, using a, b and angle:
[pic]
Special parallelograms
If all angles are 900 degrees, then it is also called a rectangle. If all angles are 900 degrees and the lines are of the same length, then it is also called a square. If all sides are of the same length, then it is also called a rhombus.
Example 3: The sides of a 900 angle with the same...
...QUADRILATERALS
IMPORTANT TERMS, DEFINITIONS AND RESULTS
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Sum of the angles of a quadrilateral is 360°. A diagonal of a parallelogram divides it into two congruent triangles. In a parallelogram, (i) opposite sides are equal (ii) opposite angles are equal (iii) diagonals bisect each other A quadrilateral is a parallelogram, if (i) opposite sides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (iv) a pair of opposite sides is equal and parallel
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Diagonals of a rectangle bisect each other and are equal and viceversa. Diagonals of a rhombus bisect each other at right angles and viceversa. Diagonals of a square bisect each other at right angles and are equal, and viceversa. The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half of it. A line through the midpoint of a side of a triangle parallel to another side bisects the third side. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral, in order, is a parallelogram.
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SUMMATIVE ASSESSMENT MULTIPLE CHOICE QUESTIONS
PR AK AS HA N
(a) 90° (b) 180°
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[1 Mark]
A. Important Questions
1. Two consecutive angles of a parallelogram are in the ratio 1 : 3. Then the smaller angle is : (a) 50° (b) 90° (c) 60° (d) 45° 2. A quadrilateral is a parallelograms if : (a) both pairs...
...here is a quadrilateral.
A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, so is BD.
TYPES & PROPERTIES OF QUADRILATERALS
There are seven types of quadrilaterals that can be divided into two groups: parallelograms and other quadrilaterals.
1. Parallelograms
Quadrilaterals are called parallelograms if both pairs of opposite sides are equal and parallel to each other. Different parallelograms and their properties.
a) Parallelogram
Opposite sides of a parallelogram are parallel and equal in length.
Opposite angles are equal in size.
b) Rectangle
Opposite sides of a rectangle are parallel and equal in length,
All angles are equal to 90°.
c) Square
Opposite sides of a square are parallel and all sides are equal in length,
All angles are equal to 90°.
d) Rhombus
All sides of a rhombus are equal in length,
Opposite sides are parallel,
Opposite angles of a rhombus are equal,
The diagonals of a rhombus bisect each other at right angles.
Rectangles, squares and rhombuses are parallelograms.
2.Other Quadrilaterals
Other quadrilaterals include trapeziums, kites and irregular quadrilaterals.
a) Trapezium
A trapezium has one pair of opposite sides parallel.
A regular trapezium has nonparallel sides...
...8th QUADRILATERAL AND PARALLELOGRAM
1. Prove that in a parallelogram, the opposite sides are equal and the
opposite angles are equal.
2. Prove that diagonals of a rhombus bisect each other at right
angles.
3. Two adjacent angles of a parallelogram are as 2:3. Find the
measure of each of its angles.
4. Prove that the diagonals of a square are equal and bisect each other
at right angles.
5. If an angle of a parallelogram is twothird of its adjacent angle,
then what is the smallest angle of the parallelogram?
6. The length of diagonals of a rhombus are 16cmand12cm. Find the
length of each side of the rhombus.
7. The length and breadth of a rectangle are in the ratio 4:3. If the
diagonals measures 25cm, then what is the perimeter of the
rectangle?
8. If one angle of a parallelogram is 24less than twice the smallest
angle, then what is the largest angle of the parallelogram?
www.jsuniltutorial.weebly.com/
Page 1
8th QUADRILATERAL AND PARALLELOGRAM
9. Prove that any two adjacent angles of a parallelogram are
supplementary.
10.
The sides of a rectangle are in the ratio 5:4and its perimeter is
90cm. Find its length and breadth.
11.
Prove that the sum of exterior angles of a quadrilateral is360
12.
Three angles of a quadrilateral are equal and the measure of
the fourth angle is 120. Find the measure of each...
...MATH FINAL EXAM
STUDY GUIDE
Tips to remember:
1) To solve equations, use inverse (opposite) operations to find the solution and don’t forget to check.
Ex: x + 12 = 42 Ex 2: = 11
 12  12 x 7 = 11 x 7
X = 30 is the solution n = 77 is the solution
2)  To change Percent Fraction: place the number over 100 then do lowest terms.
 To Change Fraction Percent: use proportion ( ) and cross multiply
 To change from decimal to percent and percent to decimal use: d p
3) MEAN: Add, and then divide by the total number
MEDIAN: Don’t forget to arrange in order before searching for the middle number
MODE: There can be one mode, more than one, or none.
RANGE: Greatest number – smallest number
4) Exploring solid figures: Face: flat side 
Vertex: point ( corner)  Check: V+F –E= 2
Egde: Line 
Pyramid: PRISM:
1 base, others are triangles 2 identical bases
5) Area of a Rectangle: length (l) x width (w) Perimeter = 2 (l + w)
Ex: l = 5 cm, w = 2 cm. A= 5 x 2 = 10 cm2...
...NAME: Eden Barrera Rodriguez
COURSE: BEEd General Education DATE: 11.26.2012
MATH LESSON PLAN:
KINDS OF PLANE FIGURES
OBJECTIVES:
At the end of 45 minutes discussion, the students will be able to:
* Identify the different kinds of plane figures
* Draw plane figures correctly
* Appreciate the shapes around us. Show awareness to the things around us.
PROCEDURE:
A. MATERIALS: white board marker (black)
Visual aid (brightcolored cartolina)
Pictures (shapes)
B. DISCUSSION
B.1 RECAP/MOTIVATION
1. Give each student a blank white sheet of paper.
a. Instruct students to cut figures like triangle, square, rectangle, circle, parallelogram and trapezoid.
b. Tell the students to color it with different colors for a few minutes.
c. Show students examples.
2. Ask the students to tell what the names of their figures are.
3. Tell the students that today we are going to learn about what are the kinds of plane figures are.
B.2 LESSON PROPER
Shapes can be polygons → A closed plane figure made up of line segments. 
A polygon with 3 sides

A 4sided figure with 4 right angles and opposite sides parallel and the same length 
A 4sided figure that has 4 equal sides and 4 right angles 
A 4sided figure that has exactly one pair of parallel sides 
A 4sided figure with 2 pairs of parallel sides and all sides the same length  A circle is also a plane figure. A circle is a plane...
...2015
Math Curse By: Jon Scieszka and Lane Smith
Math Curse, written by Jon Scieszka and Lane Smith, takes us on a journey with a small child who is cursed by math. His teacher’s name is Mrs. Fibonacci, who was a well know mathematician who connected a mathematical sequence found in nature. Of course Mrs. Fibonacci told her class and this child how easily math can be seen in the outside world. Our main character goes on amath rampage that drives him crazy. Scieszka and Smith do a great job a combining mathematical concepts as well as rhymes and brain games. The book is continuously rhyming accompanied by humorous art work that gives the story a kind of flow. Want a little bit of a challenge? Try answering a number of math questions asked throughout the book. The math used consisted mainly of patterns if not basic math of a 3rd grader. Fractions were mentioned but as any 3rd grader would be our main character was terrified of them. So much so that he may have considered answering the question in French instead of math.
Overall the book seemed good for the target audience. There was appealing art work on each page, as well as rhymes. The Rhyming scheme made a big difference because it made the story have a sense of flow. Our authors also made the story interesting for an older more sophisticated audience with the introduction of Ms. Fibonacci who...
...Article Review 1
DeGeorge, B., Santoro, A. (2004). “Manipulatives: A HandsOn Approach to Math.” Principal, 84 (2), (2828).
This article speaks about the importance and significance of the use of manipulatives in the classroom, specifically in the subject of math. Manipulatives have proven to be valuable when used in a math class and are even more valuable to the children when they are young, and are learning new math concepts. Students are able to physically visualize the math concepts and gain knowledge because they understand what they’re learning a whole lot better and they also are able to gain insights on those concepts. Different examples of manipulatives may include counting with beans or M&M’s, using pattern blocks, puzzles, tangrams, and flash cards, just to name a few.
Using manipulatives in a math class are beneficial to both the student and the teacher because the teacher is able to explain the concepts to the students in a much easier manner using the handson technique, rather than explaining it verbally. It’s especially beneficial to the student because by incorporating these manipulatives into their learning process, they are able to pick up the concepts much quicker and in a way that they better understand, yet are having fun while doing it. When they have the concepts down, the students’ selfesteem goes up and they feel encouraged to keep on going.
After...
...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between nonmoving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...