CBSE:10th Math :Chapter Triangles : Solved Concept builder theorems




If a line divides any two sides of a triangles proportionally then the line is parallel to the third side
Statement: If a line divides any two sides of a triangles proportionally (in same ratio), then the line is parallel to the third side.

Proof: We are given ABC 
AD / BD = AE / CE

We have to prove: DE is parallel to BC

Let DE's not parallel to BC then an another line DE' is parallel to BC.

Now

AD / BD = AE / CE [Given]

And AD / BD = AE' / CE' [Thales Theorem]

Therefore AE / CE = AE' / CE'

i.e. AE / CE + 1 = AE' / CE' + 1

i.e. AE + CE / CE = AE' + CE' / CE' 

i.e. CE = CE'

But this is not possible until E and E' is coincident.

Thus, our assumption is wrong and DE is parallel to BC.
X Triangles :Criteria for Similarity of Triangles Solved: 

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  1. J.Sunil SirJune 11, 2012 at 8:13 AM

    X Similar Triangle test paper-1
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    X Similar Triangle test paper-2
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  2. CA bhaiyaJanuary 19, 2026 at 1:37 AM

    Students aiming to score well in board exams need both conceptual clarity and consistent practice. CA Bhaiya combines these two aspects by offering structured explanations, smart shortcuts, and regular revision strategies. His teaching style is calm, clear, and student-friendly, which makes learning enjoyable. With class 10 maths by CA Bhaiya, learners can improve accuracy, reduce exam fear, and develop a strong understanding of all important chapters.

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