ABCD is a trapezium in which AB || DC and its diagonals intersect each other at O. Using Basic Proportionality theorem prove that

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Trapezium ABCD is shown in the figure below: Consider △OAB and △OCD, ∠AOB = ∠COD [Vertically opposite angles are equal] ∠OBA = ∠ODC [Alternate angles are equal] ∠OAB = ∠OCD [Alternate angles are equal] Therefore, by AA rule of similarity △OAB ~ △OCD, Hence, proved that

Mathematics

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at O. Using Basic Proportionality theorem prove that

Similarity

Related Questions

In the adjoining figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

In the adjoining figure, AD is bisector of ∠BAC. If AB = 6 cm, AC = 4 cm and BD = 3 cm, find BC.

Given that △s ABC and PQR are similar. Find :
(i) the ratio of the area of △ABC to the area of △PQR if their corresponding sides are in the ratio 1 : 3.
(ii) the ratio of their corresponding sides if area of △ABC : area of △PQR = 25 : 36.

Mathematics

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at O. Using Basic Proportionality theorem prove that

Similarity

Related Questions

In the adjoining figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

In the adjoining figure, AD is bisector of ∠BAC. If AB = 6 cm, AC = 4 cm and BD = 3 cm, find BC.

Given that △s ABC and PQR are similar. Find :(i) the ratio of the area of △ABC to the area of △PQR if their corresponding sides are in the ratio 1 : 3.(ii) the ratio of their corresponding sides if area of △ABC : area of △PQR = 25 : 36.

Given that △s ABC and PQR are similar. Find :
(i) the ratio of the area of △ABC to the area of △PQR if their corresponding sides are in the ratio 1 : 3.
(ii) the ratio of their corresponding sides if area of △ABC : area of △PQR = 25 : 36.