Exam Questions & Step-by-Step Markschemes (73 Problems)
Question 1 • 2024
5 Marks
State and prove the Basic Proportionality Theorem (Thales' Theorem): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Answer: \frac{AD}{DB} = \frac{AE}{EC} \quad \text{(Q.E.D.)}
Question 2 • 2023
3 Marks
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Answer: 3 AB^2 = 4 AD^2 \quad (\text{Proved})
Question 3 • 2024
5 Marks
State and prove Basic Proportionality Theorem (Thales' Theorem).
Answer: \text{Hence Proved, } \frac{AD}{DB} = \frac{AE}{EC}
Question 4 • 2023
5 Marks
Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Answer: \frac{AD}{DB} = \frac{AE}{EC}
Question 5 • 2025
1 Marks
Which of the following statements is incorrect?
Answer: (B) A square and a rhombus of the same area are always similar.
Question 6 • 2025
1 Marks
The measurements of \triangle LMN and \triangle ABC are shown in the figure given below. The length of side AC is : <div style="text-align: center; margin: 12px 0;"><img src="/images/cbse10/25M_30-3-1_q11_q_1.png" alt="Figure" style="max-width: 100%; max-height: 260px; border-radius: 8px;" /></div>
Answer: Option (C) : 8 \operatorname{cm}