P, Q and R are midpoints of sides AB, AC and BC respectively. Find the ratio between the Area of ΔPQR and Area of ΔABC.

Option 1 : 1 : 4

**Calculation:**

By mid point theorem,

PQ || BC

PQ = 1/2 × BC

RC = PQ

∠AQP = ∠QCR ----(alternate angles)

ΔAQP and ΔQCR are congruent triangles by SAS test.

Area of ΔAQP = Area of ΔQCR

Similarly using SAS congruency test and midpoint theorem we can prove area of all four triangles are same.

Area of ABC = 4 × Area of PQR

**∴ Area of ΔPQR : Area of ΔABC = 1 : 4**

__Important Points__

SAS congruency test = If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS test.