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Maharashtra State BoardSSC (English Medium) 10th Standard

In fig., AB ⊥ BC and DC ⊥ BC, AB = 6, DC = 4 then (A(ΔABC))/(A(ΔBCD)) = ?

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Question

In fig., AB ⊥ BC and DC ⊥ BC, AB = 6, DC = 4 then `(A(ΔABC))/(A(ΔBCD))` = ?

Sum
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Solution

ΔABC and ΔBCD have same base BC.

∴ `(A(ΔABC))/(A(ΔBCD)) = (AB)/(DC)`   ...[Triangles having equal base]

∴ `(A(ΔABC))/(A(ΔBCD)) = 6/4`   ...[Given]

∴ `(A(ΔABC))/(A(ΔBCD)) = 3/2`

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Chapter 1: Similarity - Q.2 (B)

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Prove that, The areas of two triangles with the same height are in proportion to their corresponding bases. To prove this theorem start as follows:

  1. Draw two triangles, give the names of all points, and show heights.
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In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.


Given: PQ ⊥ BC, AD ⊥ BC

Now, A(ΔPQB)  = `1/2 xx square xx square`

A(ΔPBC)  = `1/2 xx square xx square`

Therefore, 

`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`

= `square/square`


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