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Grade 9 Parallelograms Math (3rd Semester) Cheat Sheet by

Lessons i remember from Math in the 3rd Semester as a Student of FTHS.

QUADRI­LATERAL

Is a Four sided Polygon, having 4 Edges(­sides)
Derived from latin words "­Qua­dri­" a Variation of Four and "­Lot­us" meaning Side.
another name for it is "­tet­rag­on"
Derived from the Greek word "­Tet­ra" meaning four and "­Gon­" meaning Corner or Angles

Properties of a Parall­elogram

Consec­utive Angles are Supple­mentary
Parallel Sides are Congruent
Opposite Angles are Congruent
Diagonals Bisect each other
Diagonals Bisect the Parall­elogram into two Congruent Triangles
Diagonals are Congruent

PROVING THEOREMS and POSTULATES

VAT Vertical Angles Theorem
Vertical angles are Congruent
AAP Angle Addition Postulate
if three Sides of one Triangles are Congruent to the Corres­ponding parts of another. then triangles are Congruent
CPCTC
Corres­ponding Parts of Congruent Triangles are Congruent
LC Congruence Theorem
if the Leg of another Right Triangle is Congruent, then the two Right Triangles are Congruent

TRAPEZOID

Is a Quadri­lateral in which are and only one pair of opposite sides are parallel
The Parallel sides of a trapezoid are called BASES
The Non-Pa­rallel sides are Called LEGS
The pair of angles formed by a base and legs are called BASE ANGLES
if the LEGS of the Trapezoid are Congruent, then the Trapezoid is called an ISOSCELES TRAPEZOID
 

KINDS OF QUADRI­LATERAL

PARALL­ELOGRAM a quadri­lateral with two pairs of parallel sides
RHOMBUS a quadri­lateral with two pairs of congruent sides
RECTANGLE a quadri­lateral with four right angles
SQUARE a quadri­lateral with four congruent angles and sides
TRAPEZOID a quadri­lateral with one pair of parallel sides
KITE a quadri­lateral with two distinct pairs of consec­utive sides that are congruent

SPECIAL PROPERTIES

Properties
Parall­elogram
Rectangle
Opposite Sides are Parallel
True
True
Opposite Angles are Congruent
True
True
Consec­utive Angles are Supple­mentary
True
True
Diagonals Bisect each other
True
True
Either Diagonals form Two Congruent Triangles
True
True
Pairs of Opposite Sides are Congruent and Parallel
True
True
Opposite Sides are Congruent
True
True
Diagonals are perpen­dicular
False
False
Diagonals Bisect a pair of Opposite Angles
False
False
Diagonals are Congruent
False
True
Diagonals are Both Perpen­dicular and Congruent
False
False

ISOSCELES TRAPEZOID

an Isosceles Trapezoid features some special properties
Legs are Congruent
Base Angles are Congruent
Diagonals are Congruent

Median of Trapezoid

is a Segment which Joints the Mid Points of the Non-Pa­rallel Sides.
It is Parallel to the Bases and has a Length equal to 1/2 the sum of the length of the bases
(Upper Base + Lower Base)/2
 

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  • Published: 7th April, 2023

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