A square of side is divided into nine equal smaller squares by drawing two horizontal…
MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A square of side 6cm is divided into nine equal smaller squares by drawing two horizontal and two vertical lines each 2cm apart. In each of the four corner small squares, a diagonal is drawn from the bottom-left vertex to the top-right vertex of that square. Answer the questions below:
(i) How many right-angled isosceles triangles of side 2cm are formed in the entire design?
(ii) Verify that all triangles counted in part (i) are congruent.
(iii) If one such triangle is cut out and placed over any other triangle of the same kind in the design, will it completely cover it? Give a reason for your answer.