abcd Is a trapezium in which AB||DC and diagonals interest at O. show AO/BO=CO/DO by similarity of triangles
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abcd Is a trapezium in which AB||DC and diagonals interest at O. show AO/BO=CO/DO by similarity of triangles
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Answer:
see below
Step-by-step explanation:
Given:
ABCD is a trapezium and AB∥DC
To Prove: AOBO=CODO
Construction:
Draw OE∥DC such that E lies on BC.
Proof:
In △BDC,
By Basic Proportionality Theorem,
BOOD=BEEC............(1)
Now, In △ABC,
By Basic Proportionality Theorem,
AOOC=BEEC............(2)
∴ From (1), and (2),
AOOC=BOOD
i.e., AOBO=CODO