Triangle ABC is similar to triangle DEF meaning their corresponding angles are equal and their corresponding sides are proportional in length. This similarity implies that the two triangles have the same shape but may differ in size. Similarity is denoted by the symbol ~ and is based on angle-angle-angle or side-angle-side properties.
Class 10 Maths Chapter 6 Triangles is a key topic for CBSE Exam 2024-25. It covers concepts like similarity and congruence of triangles along with important theorems. Students will learn about angle-side relations area ratios and applications of triangles. This chapter strengthens problem-solving skills and is essential for scoring well in geometry and related questions.
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When two triangles are similar (ΔABC ~ ΔDEF), their areas and sides follow a particular mathematical relationship:
If area ratio = m:n, then side ratio = √m:√n
Given:
– ΔABC ~ ΔDEF
– ar(ABC):ar(DEF) = 16:25
Therefore:
1. The side ratio is obtained by square root of the area ratio
2. Side ratio = √16:√25
3. Simplifying: 4:5
AB:DE = 4:5
This relationship holds because:
– Area ratio = (Side ratio)²
– Suppose side ratio = x:y, then area ratio = x²:y²
– In a similar vein, if area ratio = m:n, then side ratio = √m:√n
– Now, in this example, √16:√25 = 4:5
The above mathematical equivalence applies to every pair of similar triangles because area ratio is always equal to the square of ratio of the respective sides.
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