AD is the median of triangle ABC. If P is any point on AD, then which one of the following is correct?
- A. Area of triangle PAB is greater than the area of triangle PAC
- B. Area of triangle PAB is equal to the area of triangle PAC ✓
- C. Area of triangle PAB is one-fourth of the area of triangle PAC
- D. Area of triangle PAB is half of the area of triangle PAC
Correct Answer: B. Area of triangle PAB is equal to the area of triangle PAC
Explanation
A median divides a triangle into two triangles of equal area. Thus, Area(\Delta ABD) = \text{Area}(\Delta ACD). Since PD is the median of \Delta PBC, Area(\Delta PBD) = \text{Area}(\Delta PCD). Subtracting the lower triangles from the larger ones yields Area(\Delta PAB) = \text{Area}(\Delta PAC).
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