Question

ABCD is a trapizum AB is 5 CM and cd is 10 CM and they are bisect at point o.
QUE- the two triangular regions AOB AND cod are : a) similar by AA criteria
b) similar by SAS criteria
c) similar by RHS criteria
d ) not similar
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Answer 1

Step-by-step explanation:

Solution:

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Let's construct a diagram according to the given question.

Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD

In trapezium ABCD,

AB is parallel to CD and AB = 2 CD ---------- (1)

Diagonals AC and BD intersect at ‘O’

In ΔAOB and ΔCOD,

∠AOB = ∠COD (vertically opposite angles)

∠ABO = ∠CDO (alternate interior angles)

⇒ ΔAOB ~ ΔCOD (AA criterion)

⇒ Area of ΔAOB / Areaof ΔCOD = (AB)2 / (CD)2 [Theorem 6.6]

(2CD)2 / (CD)2 = 4CD2 / CD2 = 4 / 1 [From equation (1)]

Thus, Area of ΔAOB : Area of ΔCOD = 4:1