Mathematics Dictionary Dr. K. G. Shih

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Quadrilateral and Parallelogram

Subjects

Symbol Defintion Example GE = geater and equal

GE 06 00 | - Outlines GE 06 01 | - Introduction diagrams GE 06 02 | - Square : Properties GE 06 03 | - Rectangle : Properties GE 06 04 | - Parallelogram : Properties GE 06 05 | - Rhombus : Properties GE 06 06 | - Change quadrilateral to equal area of trinagle GE 06 07 | - GE 06 08 | - GE 06 09 | - GE 06 10 | - Change square to equal area triangle GE 06 Q11 | - Change quadrilateral to equal area triangle GE 06 12 | -

Answers

GE 06 01. Introduction Diagrams Study | Various shapes of quadrilaterals Properties of quadrilateral It has 4 sides and 4 angles Sum of internal angles = 2*pi Sum of external angles = 2*pi Join the mid points of 4 sides forming a parallelogram If 4 vertices A,B,C,D are on same circle It is called four points being concylic Then sum of the opposite angles = 180 degrees Go to Begin GE 06 02. Square : Properties Four sides are equal and each side is a The area is a^2 Each internal angle is 90 degrees Diagonals bisect each other equally Diagonals are perpendicular each other Diagonals bisect the opposite angles It has four symmetrical axese Two are the diagonals Two are the bisectors of opposite sides Opposite sides are parallel Go to Begin GE 06 03. Rectangle : Properties Opposite sides are equal and the sides are a, b, a, b The area is a*b Each internal angle is 90 degrees Diagonals divide each other equally Diagonals are not perpendicular each other Diagonals bisect the opposite angles It has two symmetrical axese : Bisectors of opposite sides Opposite sides are parallel Go to Begin GE 06 04. Parallelogram : Properties Opposite sides are parallel and equal and the sides are a, b, a, b The area is a*h and h is the distance between two opposite sides Each internal angle is not 90 degrees. But the opposite angles are equal Ten neighbour angles are supplementary Diagonals divide other diagonals equally Diagonals are not perpendicular each other Diagonals do not bisect the opposite angles It has no symmetrical axese Opposite sides are parallel Go to Begin GE 06 05. Rhombus : Properties Four sides are equal and the sides are a, a, a, a The area is diagonal times diagonal Each internal angle is not 90 degrees. But the opposite angles are equal The neighbour angles are supplementary Diagonals Diagonals bisect other diagonal Diagonals are perpendicular each other Diagonals bisect the opposite angles It has two symmetrical axese : Two diagonals Opposite sides are parallel Home work Compare the square with rhombus Go to Begin GE 06 06. Change quadrilateral to equal area triangle Method and proof Constuction a. Draw a quadrilateral ABCD b. Draw line DE parallel to AC c. Produce BC and meet DE at P d. Draw triangle ABP e. Area ABP = Area ABCD proof a. Since DP parallel to AC b. Hence area APC = area ADC c. Area ABP = area APC + Area ABC = area ADC + area ABC = area ABCD Go to Begin GE 06 07. Answer Go to Begin GE 06 08. Answer Go to Begin GE 06 09. Answer Go to Begin GE 06 10. Example : Change square to equal area triangle Construction Draw a square ABCD Join diagonal AC Draw line DQ parallel to AC Produce BC to meet DQ at P Join AP Then Area of square ABCD = area of triangle ABP Prove that area ABCD = area ABP Area ABCD = area ABC + area ACD Area ABP = area ABC + area ACP Triangle ACD and ACP have same base and same height. Hence area ACD = ACP Hence area ABCD = area ABP Go to Begin GE 06 11. Example : Change quadrilateral to equal area triangle Construction Draw a quadrilateral ABCD Join diagonal AC Draw line DQ parallel to AC Produce BC to meet DQ at P Join AP Then Area of quadrilateral ABCD = area of triangle ABP Prove that area ABCD = area ABP Area ABCD = area ABC + area ACD Area ABP = area ABC + area ACP Triangle ACD and ACP have same base and same height. Hence area ACD = ACP Hence area ABCD = area ABP Go to Begin GE 06 00. Outlines Properties Properties of rhombus Construction Quadrilateral is changed to equal area triangle Square is changed to equal area triangle Go to Begin

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