In `DeltaABC`, a point P on BC divided BC in the ratio 1:1. what is the line segment joining vertex A and P called ?

Options

A. Median
B. Altitude
C. Side
D. None of the above

Answer

To solve the question, we need to analyze the triangle ABC and the point P on side BC. Here’s the step-by-step solution:

### Step 1: Identify the Triangle and the Point
We have triangle ABC, and a point P is located on side BC. The problem states that point P divides BC in the ratio 1:1.

**Hint:** Remember that a ratio of 1:1 means that the two segments created by point P are equal in length.

### Step 2: Understand the Implication of the Ratio
Since P divides BC in the ratio 1:1, it means that the lengths of segments BP and PC are equal. Therefore, point P is the midpoint of segment BC.

**Hint:** A midpoint is a point that divides a line segment into two equal parts.

### Step 3: Identify the Line Segment
Now, we consider the line segment joining vertex A (the top vertex of the triangle) to point P (the midpoint of BC). This line segment is denoted as AP.

**Hint:** When connecting a vertex of a triangle to the midpoint of the opposite side, it has a special name.

### Step 4: Define the Line Segment
The line segment AP is called the **median** of triangle ABC. A median of a triangle is defined as the line segment that connects a vertex to the midpoint of the opposite side.

**Hint:** Remember that every triangle has three medians, one from each vertex.

### Conclusion
Thus, the line segment joining vertex A and point P is called the **median** of triangle ABC.

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