Question

As shown in the given figure, a student drew ∆ABC using five parallel lines of a notebook. Then he found the centroid G of the triangle. How will you decide whether the location of G he found, is correct.

Answer 1

Draw seg AP ⊥ seg PE and seg EQ ⊥ seg QC.

Side AP || side EQ and AC is their transversal. 

∴ ∠PAE ≅ ∠QEC …(i) [Corresponding angles] 

In ∆ APE and ∆ EQC, 

∠PAE ≅ ∠QEC …[From (i)] 

∠APE ≅ ∠EQC … [Each angle is of measure 90°] 

side PE ≅ side QC …. [Perpendicular distance between parallel lines] 

∴ ∆ APE ≅ ∆ EQC … [By AAS test] 

∴ AE = EC … [Corresponding sides of congruent triangles] 

∴ E is the midpoint of AC. 

∴ seg BE is the median. Similarly, seg CF is the median. 

Since, the medians of a triangle are concurrent. 

∴ G is the centroid of ∆ABC.