In ` A B C ,D` is the mid-point of `A B ,P` is any point of `B CdotC Q P D` meets `A B` in `Q` . Show that `a r( B P Q)=1/2a r( A B C)dot` TO PROVE : `a r( B P Q)=1/2a r( A B C)` CONSTRUCTION : Join CD.

Explanation

To prove that the area of triangle \( BPQ \) is equal to half the area of triangle \( ABC \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Midpoints:**
- Given triangle \( ABC \), point \( D \) is the midpoint of side \( AB \). This means \( AD = DB \).

2. **Construct Line Segment:**
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