Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two ОА OC OB OD triangles, show that OD​

Answer 1

Answer:

ABCD is a trapezium with AB∥CD and diagonals AB and CD intersecting at O.

Explanation:

=In △OAB and △OCD

=∠ABO=∠CDO           [ Alternate angles ]

=∠BAO=∠OCD           [ Alternate angles ]

=∴   △OAB∼△OCD   [ AAA similarity ]

=We know that if triangles are similar, their corresponding sides are in proportion.

=OA/OC=OB/OD     hence proved