parallelogram

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about parallelogram

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By: n.ibrhim (38 month(s) ago)

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SANDEEP KUMARIX -B ROLL NO-41 : 

SANDEEP KUMARIX -B ROLL NO-41

POWERPOINT PRESENTATION ON PARALLELOGRAM : 

POWERPOINT PRESENTATION ON PARALLELOGRAM

PARALLELOGRAM : 

PARALLELOGRAM DEFINITION ELEMENTS PROPERTIES EXAMPLES POINTS TO REMEMBER

DEFINITION : 

DEFINITION A PARALLELOGRAM IS A QUADILATERAL WHOSE OPPOSITE SIDES ARE PARALLEL.

ELEMENTS : 

ELEMENTS FOUR SIDES AND FOUR ANGLES SOME OF THESE ARE EQUAL OPPOSITE SIDES FORM ANOTHER PAIR OF OPPOSITE SIDES OPPOSITE ANGLES FORM ANOTHER PAIR OF OPPOSITE ANGLES ADJACENT SIDES ADJACENT ANGLES

PROPERTIES : 

PROPERTIES THE OPPOSITE SIDES OF A PARALLELOGRAM ARE OF EQUAL LENGTH THE OPPOSITE ANGLES OF A PARALLELOGRAM ARE OF EQUAL MEASURE THE ADJACENT ANGLES IN A PARALLELOGRAM ARE SUPPLEMENTARY THE DIAGONALS OF A PARALLELOGRAM BISECT EACH OTHER AT THE POINT OF THEIR INTERSECTION, OF COURSE! A DIAGNOL OF A PARALLELOGRAM DIVIDES IT INTO 2 CONGRUENT TRIANGLES

Example-1(property-1) : 

Example-1(property-1) In a parallelogram ,the opposite sides have same length. Therefore , PQ=SR=12cm and QR=PS=7cm So, Perimeter=PQ+QR+SR+PS =12cm+7cm+12cm+7cm= 38cm 12 cm 7cm Q R S P

Example-2(property-2) : 

Example-2(property-2) The opposite angles of a parallelogram are of equal measure. If AC and BD are diagnols of the parallelogram, we find that Angle 1= Angle 2 And Angle 3= Angle 4 B’COZ Triangle ABC = Triangle CDA This shows Angle B = Angle D & Angle A= Angle C C D 2 3 4 1 A B

Example-3(property-3) : 

Example-3(property-3) The adjacent angles in a parallelogram are supplementary. Angle A=70 Then Angle C =70 B’COZ Angle A& Angle C are opposite angles of parallelogram Since Angle A & Angle B are supplementary Angle B=180-70=110 SO, Angle D =110 SINCE Angle B& Angle D are supplementary. A B C D 70

Example-4(property-4) : 

Example-4(property-4) THE DIAGONALS OF PARALLELOGRAM BISECT EACH OTHER AT THE POINT OF THEIR INTERSECTION, OF COURSE! AO=OC BO=OD SO , O is the point of intersection for both the diagonals A B C D O

Example-5(property-5) : 

Example-5(property-5) A DIAGONAL OF A PARALLELOGRAM DIVIDES IT INTO 2 CONGRUENT TRIANGLES Diagonal AC divides the parallelogram into two triangles i.e. Triangle ABC & Triangle AD both the triangles are congruent to each other A B C D

Points to Remember : 

Points to Remember Opposite sides are equal Opposite angles are equal Diagonals bisect each other