In ΔABC if AD ⊥ BC then AD is the altitude from vertex A to side BC. This implies that AD forms a right angle with BC and divides the triangle into two right triangles. The property is essential in geometry for calculating area and applying the Pythagorean theorem when needed.
Class 10 Maths Chapter 6 Triangles is a vital topic for the CBSE Exam 2024-25. It covers similarity and congruence of triangles along with important theorems like Pythagoras theorem and basic proportionality theorem. The chapter focuses on properties of triangles and their applications in solving problems. Understanding these concepts is crucial for scoring well and excelling in geometry-related questions during the exam.
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When AD is the altitude from vertex A to side BC, it divides ΔABC into two right triangles, ΔABD and ΔACD. Using the property of the area of a triangle, we know that the area can be expressed in two ways:
1. Area = (1/2) × base × height = (1/2) × BC × AD.
2. Area = (1/2) × AB × AC × sin(∠BAC).
Equating the two expressions for the area:
(1/2) × BC × AD = (1/2) × AB × AC × sin(∠BAC).
Since sin(∠BAC) = AD / AB (from the definition of sine in ΔABD), substituting this value simplifies the equation to:
BC × AD = AB × AC.
Thus, the correct answer is AB × AC = BC × AD.
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