Q1. [1] § 6.4 Criteria for Similarity of Triangles
In the given figure, $DE \parallel BC$. If $AD = 2$ units, $DB = AE = 3$ units and $EC = x$ units, then the value of $x$ is:
- (a) $2$
- (b) $3$
- (c) $5$
- (d) $\frac{9}{2}$
Previously asked in CBSE board exam
2023 30/2/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer
By Basic Proportionality Theorem (DE ∥ BC):
$$\frac{AD}{DB} = \frac{AE}{EC}$$
$$\frac{2}{3} = \frac{3}{x}$$
$$x = \frac{3 \times 3}{2} = \frac{9}{2}$$
The value of $x$ is $\dfrac{9}{2}$. (d)
Source: Chapter 6, Section 6.3 (Theorem 6.1 – Basic Proportionality Theorem)
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Explanation
- The Basic Proportionality Theorem (Thales' Theorem) states: if DE ∥ BC, then $\frac{AD}{DB} = \frac{AE}{EC}$.
- Simply substitute the given values and cross-multiply — a common 1-mark MCQ technique.
- Students often make the error of writing $\frac{AD}{AB}$ instead of $\frac{AD}{DB}$; always use the segment ratios (part : other part), not part : whole.
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