Question

Line segments joining the midpoints M and N of the parallel sides AB and CD resp. of Trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD = BC

Answer 1

given
ABCD is a trapezium
M is the mid point of AB
N is the mid point of CD

Construction
Join B to N
Join A to N
Proof
Consider ΔAMN and ΔBMN
∠AMN=∠BMN=90
AM=BM (M is the midpoint of AB)
MN=MN(common)
ΔAMN congruent to ΔBMN(SAS congruence rule)


Consider ΔADN and ΔBCN
DN=CN(N is the midpoint of CD)
AN=BN(CPCT)
∠MNA=∠BNM(CPCT)   1
∠MNC=∠MND= 90        2
2-1
∠MND-∠MNA=∠MNC-∠BNM
∠AND=∠BNC
ΔAND congruent to ΔBNC
AD=BC(CPCT)
Hence proved


Sincerely
Your friend

Answer 2

Answer:

Step-by-step explanation:

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