Situation: One of your classmate is absent during the discussion of properties of a parallelogram. Quadrilaterals and theorems on different kind of quadrilaterals. As a help, you will make a letter for him that will discuss the said topics. You can also include illustrations of the following qudrilaterals.
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Situation: One of your classmate is absent during the discussion of properties of a parallelogram. Quadrilaterals and theorems on different kind
Answer:
LETTER TO MY CLASSMATE
Dear Classmate,
Hi classmate this is our discussion of properties of a parallelogram. Quadrilaterals and theorems on different kind of quadrilaterals. I hope I could help you on your study.
Properties of Parallelogram
If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called Parallelogram. The properties of a parallelogram are as follows:
The opposite sides are parallel and congruent
The opposite angles are congruent
The consecutive angles are supplementary
If any one of the angles is a right angle, then all the other angles will be at right angle
The two diagonals bisect each other
Each diagonal bisects the parallelogram into two congruent triangles
The Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals. It is also called parallelogram law
Formulas (Area & Perimeter)
The formula for the area and perimeter of a parallelogram is covered here in this section. Students can use these formulas and solve problems based on them.
Area of Parallelogram
Area of a parallelogram is the region occupied by it in a two-dimensional plane. Below is the formula to find the parallelogram area:
Area = Base × Height
What is a quadrilateral?
As Euclidean geometry is the best accepted form of Geometry in today's world,we will go with the definition from Euclidean geometry itself.According to Euclidean Plane Geometry,a quadrilateral is a polygon with four edges and four vertices.
Origin of the Word
The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."
Important note : The sum of all the angles of a quadrilateral always give 360° when added together.
The Theorems
If the quadrilateral is a parallelogram,the two pairs of opposite sides are equal.
Converse : If the two pairs of opposite sides of a quadrilateral are equal,it is a parallelogram.
Opposite angles of a parallelogram are equal.
If in a quadrilateral,each pair of opposite angles are equal,it is a parallelogram.
If one pair of sides of a quadrilateral are equal and parallel to each other,it is a parallelogram.
If the diagonals of a quadrilateral bisect each other,it is a parallelogram.
The diagonals of a parallelogram bisect each other.
Converse : The diagonals of a parallelogram divides in into congruent triangles. (Each diagonal divides the parallelogram into two congruent triangles)
Mid - Point Theorem
The line segment that joins the mid-points of two sides of a triangle is parallel to the third side and half of the third side in measure.
Converse : The line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
Different Kinds of Quadrilaterals
Parallelogram
A quadrilateral is called a parallelogram, if both pairs of its opposite sides are parallel.
In the adjoining figure, ABCD is a quadrilateral in which
AB ∥ DC and AD ∥ BC.
So, ABCD is a parallelogram.
Rhombus
A parallelogram having all sides equal, is called a rhombus.
In the adjoining figure, ABCD is a rhombus in which
AB ∥ DC, AD ∥ BC and AB = BC = CD = DA.
Rectangle
A parallelogram in which each angle is a right angle is called a rectangle.
In the adjoining figure, ABCD is a quadrilateral in which
AB ∥ DC, AD ∥ BC and ∠A = ∠B = ∠C = ∠D = 90°.
So, ABCD is a rectangle.
Square
A parallelogram in which all the sides are equal and each angle measures 90° is called a square.
In the adjoining figure, ABCD is a quadrilateral in which
AB ∥ DC, AD ∥ BC, AB = BC = CD = DA
and ∠A = ∠B = ∠ C = ∠D = 90°.
So, ABCD is a square.
Trapezium
A quadrilateral having exactly one pair of parallel sides is called a trapezium.
In the adjoining figure, ABCD is a quadrilateral in which
AB ∥ DC.
So, ABCD is a trapezium.
Isosceles Trapezium
A trapezium whose non-parallel sides are equal is called an isosceles trapezium.
Thus, in the adjoining figure, ABCD will be an isosceles trapezium if
AD ∥ BC and AB = BC
Kite
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A quadrilateral is called a kite if it has two pairs of equal adjacent sides but unequal opposite sides.
In the adjoining figure, ABCD is a quadrilateral
AB = AD, BC = DC, AD ≠ BC and AB ≠ DC.
So, ABCD is a kite.
Step-by-step explanation: