Through the mid-point `M` of the side `C D` of a parallelogram `A B C D` , the line `B M` is drawn intersecting `A C` at `La n dA D` produced at `E` . Prove that `E L=2B Ldot`

Explanation

To prove that \( EL = 2BL \) in the given parallelogram \( ABCD \) with midpoint \( M \) on side \( CD \), we can follow these steps:

### Step 1: Identify the triangles
Consider triangles \( BMC \) and \( EMD \). We will show that these triangles are congruent.

### Step 2: Establish congruency
1. Since \( M \) is the midpoint of \( CD \), we have \( MC = MD \).
2. Angles \( BMC \) and \( EMD \) are vertically opposite angles, hence \( \angle BMC = \angle EMD \).
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