ΔABC and ΔDEF are similar which means their corresponding angles are equal and their corresponding sides are proportional in length thus they have the same shape but not necessarily the same size and this similarity is based on the fundamental property that ratios of their respective sides remain constant.
Class 10 Maths Chapter 6 Triangles is a crucial part of the CBSE Exam 2024-25 syllabus. It covers topics like similarity criteria theorems and the Pythagorean theorem. Students will learn about congruence properties and solve problems involving triangle proportions. This chapter strengthens geometric reasoning and prepares students for advanced concepts in mathematics and real-life applications in fields such as architecture and engineering.
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Since ΔABC and ΔDEF are similar, the corresponding sides of the triangles are in proportion. That is:
AB / DE = BC / EF
It is provided that 2 AB = DE, i.e.,
DE / AB = 2
Therefore, the ratio of the corresponding sides of the triangles is 1:2 (AB:DE). Based on this ratio, we can express:
BC / EF = 1 / 2
Substituting BC = 8 cm:
8 / EF = 1 / 2
Divide both sides by 8:
EF = 2
EF = 8 × 2
EF = 16 cm
So, the answer is 16 cm.
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