Q13 of 56 Page 6

ABCD is a trapezium in which AB∥CD. The diagonals AC and BD intersect at O. Prove that:

(i) Δ AOB ∼ Δ COD


(ii) If OA = 6 cm, OC = 8 cm, Find:


(a)


(b)

Given: AB∥CD


To prove: (i) Δ AOB ∼ Δ COD


(ii) If OA = 6 cm, OC = 8 cm, Find:



Theorem Used:


1) If two corresponding angles of two triangles are equal the triangles are said to be similar.


2) The ratio of the areas of two similar triangles are equal to the ratio of the squares of their heights.


Explanation:



i) We have,


AB||DC


In ΔAOB and ΔCOD (Vertically opposite angles)


∠AOB = ∠COD (Alternate interior angle)


Then, ΔAOB ~ ΔCOD (By AA similarity)


ii)


By area of similar triangle theorem.






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