Question

P and Q are mid points of AB and AC of ΔABC. Which of the following is not true?

Options

• Area of ΔBQC = Area of ΔBPC

• Area of ΔPBQ = Area of ΔPCQ

• Area of ΔAPQ = Area of ΔBOC

• Area of ΔABQ = Area of ΔBQC

Answer 1

Area of ΔAPQ = Area of ΔBOC

Explanation:

We are given:

• ΔABC, with P and Q as midpoints of AB and AC
• We need to find which statement is not true.

Step 1: Recall the midpoint theorem

• Line joining midpoints of two sides = parallel to third side and half its length
• So PQ || BC and PQ = `1/2` BC

Step 2: Compare areas of triangles

1. ΔBQC = ΔBPC

• Both triangles share BC as base and lie between same parallels (height from B or C).
• So Area(ΔBQC) = Area(ΔBPC) true

2. ΔPBQ = ΔPCQ

• Both triangles share vertex Q and line segments connecting midpoints.
• By symmetry, Area(ΔPBQ) = Area(ΔPCQ) true

3. ΔAPQ and ΔBOC

• ΔAPQ is small triangle at top (formed by connecting midpoints)
• ΔBOC is large triangle at bottom
• Clearly, ΔAPQ is smaller than ΔBOC
• So Area(ΔAPQ) ≠ Area(ΔBOC) not true

4. ΔABQ and ΔBQC

• Both share height from B or C and respective bases along triangle sides
• By midpoint theorem and proportionality, areas are equal true