in a trapezium ABCD ,AB parralel to CD and AC and BD intersect each other at M if MA=8 cm,MB=12, and MC=6 cm.find MD.
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Answered by
2
Answer:
Given: ABCD is a trapezium with AB ∥ CD and diagonals AB and CD intersecting at O.
To find: y
Firstly, we prove that ΔOAB∼ΔODC
Let ΔOAB and ΔODC
∠AOB=∠COD [vertically opposite angles]
∠OBA=∠ODC [':AB II CD with BD as transversal. alternate angles are equal]
ΔOAB=ΔOCD ['.'AB II CD with BD as transversa]. alternate angles are equal]
ΔOAB∼ΔODC [by AAA similarity]
Since triangles are similar. Hence corresponding sides are proportional.
OC
OA
=
OD
OB
=
DC
AB
⟹
OC
OA
=
DC
AB
⟹
10
y
=
30
18
⟹y=6cm
Answered by
2
Answer:
DM=16
Step-by-step explanation:
AMD & BMC (Vertically Opposite Angles)
BAM & MCD (Alternative angles)
CDM & MBA (Alternateive Angles)
CM/AM = BM/DM
6/8 = 12/DM
DM = 12×8/6
DM = 16
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