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Maharashtra State BoardSSC (English Medium) 10th Standard

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: Draw two triangles, give the names of all point

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Question

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.
  2. Write 'Given' and 'To prove' from the figure drawn.
Diagram
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Solution

i. The triangles are as follows:

ii. Given: AP = DQ

To prove: `(A(ΔABC))/(A(ΔDEF)) = (BC)/(EF)`

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Given: PQ ⊥ BC, AD ⊥ BC

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

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Therefore, 

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

= `square/square`


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