Answer :

(i) Since, each angle of a square is 900

Hence, angle ABM = angle DBC = 900


ABM + ABC = DBC + ABC


MBC = ABD (1)


In ΔMBC and ΔABD,


Angle MBC = Angle ABD (From 1)


MB = AB (Sides of square)


BC = BD (Sides of square)


Therefore,


By SAS congruence rule,



(ii) Now, we have:



And we know that adjacent sides of square are perpendicular to each other. Hence,


BD perpendicular DE


And,


AX perpendicular DE


Also,


We know that two lines perpendicular to the same line are parallel to each other.


Therefore,


BD ‖ AX


Now,


= ( and ‖gm BXYD are on same base BD and between the same parallels BD and AX)


Area (BXYD) = 2 area (ΔABD)


Area (BXYD) = 2 area (ΔMBC) (2)


(iii) ΔMBC and parallelogram ABMN are on same base MB and between the same parallels MB and NC.


Therefore,


Area (ΔMBC) = � ar (ABMN)


2 Area (ΔMBC) = Area (ABMN) = Area(BXYD) (From 2) (3)


(iv) Since, each angle of square is 900


Therefore,


Angle FCA = Angle BCE = 900


FCA + ACB = BCE + ACB


Angle FCB = Angle ACE


Now,


In ΔFCB and ΔACE,


Angle FCB = Angle ACE


FC = AC (Sides of square)


CB = CE (Sides of square)


Therefore,


By SAS congruence,



(v) It is given that AX is perpendicular to DE and CE is perpendicular to DE


and,


We know that two lines perpendicular to the same line are parallel to each other.


Hence,


CE ‖ AX


Now,


ΔACE and parallelogram CYXE are on same base CE and between the same parallels CE and AX.


Therefore,


Area (ΔACE) = 1/2 Area (CYXE)


Area (CYXE) = 2 Area (ΔACE) (4)


We had proved that


ΔFCB ΔACE


Hence,


Area (ΔACE) =Area (ΔFCB) (5)


Comparing 4 and 5, we get:


CYXE = 2 Area (ΔFCB) (6)


(vi) ΔFCB and parallelogram ACFG are on same base CF and between the same parallels CF and BG


Hence,


Area (ΔFCB) = � Area (ACFG)


Area (ACFG) = 2 Area (ΔFCB) = Area (CYXE) (Using 6) (7)


(vii) From figure:


Area (BCED) = Area (BXYD) + Area (CYXE)


Area (BCED) = Area (ABMN) + Area (ACFG) (using 3 and 7)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Revision on Angle sum Property of TrianglesRevision on Angle sum Property of TrianglesRevision on Angle sum Property of Triangles44 mins
Arc of Circle And Related IMP QsArc of Circle And Related IMP QsArc of Circle And Related IMP Qs40 mins
Surface Area and Volume of solids RevisionSurface Area and Volume of solids RevisionSurface Area and Volume of solids Revision43 mins
Circles- All kinds of QuestionsCircles- All kinds of QuestionsCircles- All kinds of Questions36 mins
Sphere and HemisphereSphere and HemisphereSphere and Hemisphere42 mins
Trigonometric Identities - Marathon Part 1Trigonometric Identities - Marathon Part 1Trigonometric Identities - Marathon Part 146 mins
Heron's Formula- Full GyanHeron's Formula- Full GyanHeron's Formula- Full Gyan46 mins
Test what you Know QuizTest what you Know QuizTest what you Know Quiz44 mins
Introduction to Lines and AnglesIntroduction to Lines and AnglesIntroduction to Lines and Angles60 mins
Speed and VelocitySpeed and VelocitySpeed and Velocity42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses