If in ΔABC, D and E are points on sides AB and AC respectively such that DE || BC and AD = 3 cm, DB = 2 cm, then AE equals:
In triangle ABC if DE is parallel to BC then by the Basic Proportionality Theorem AD divided by DB is equal to AE divided by EC and this property helps in proving similarity of triangles or finding unknown lengths in geometric problems without directly measuring them
Class 10 Maths Chapter 6 Triangles is a key topic for CBSE Exam 2024-25. It covers concepts like similarity criteria theorems and the Pythagorean theorem. Understanding triangle properties is essential for solving problems in geometry and real-life applications. Focus on practicing proofs numerical problems and constructions to score well in exams and build a strong foundation for advanced mathematics or related fields.
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In ΔABC, points D and E are on sides AB and AC respectively, with DE parallel to BC.
Given that:
– AD = 3 cm
– DB = 2 cm
– DE || BC
According to the Basic Proportionality Theorem (BPT):
– When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides in the same ratio
– Therefore, AD:DB = AE:EC = 3:2
While we know the ratio AE:EC = 3:2, we cannot determine the actual length of AE because:
1. The total length of AC is unknown
2. Without knowing AC, we cannot split it in the ratio 3:2 to find AE
3. Having just the ratio 3:2 and no information about the total length AC means there could be infinitely many possible values for AE
For example:
– If AC = 10 cm, then AE would be 6 cm
– If AC = 15 cm, then AE would be 9 cm
– If AC = 5 cm, then AE would be 3 cm
Therefore, the length of AE cannot be determined with the given information.
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