Question

Match List-I with List-II. List-I: A. Equilateral Triangle, B. Isosceles Triangle, C. Acute Angle Triangle, D. Obtuse Angle Triangle. List-II: I. A triangle with angle \(A=70^\circ\), angle \(B=60^\circ\) and angle \(C=50^\circ\). II. One angle of the triangle is \(130^\circ\). III. A triangle with each side being \(5\) cm. IV. A triangle with sides \(4\) cm, \(6\) cm and \(6\) cm.

• A. A-II, B-III, C-IV, D-I
• B. A-I, B-II, C-III, D-IV
• C. A-IV, B-I, C-II, D-III
• D. A-III, B-IV, C-I, D-II

Hint:

Equilateral means all sides equal, isosceles means two sides equal, acute means all angles less than \(90^\circ\), and obtuse means one angle greater than \(90^\circ\).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem requires us to match classification categories of triangles (based on sides and angles) to their corresponding dimensional or angle properties.

Step 2: Detailed Explanation:
Let us analyze each type of triangle listed in List-I:
• Equilateral Triangle (A): A triangle where all three sides are equal. Description III states "each side being 5 cm", which means all sides are equal. Thus, A matches III.

• Isosceles Triangle (B): A triangle where at least two sides are equal. Description IV defines a triangle with sides "4 cm, 6 cm and 6 cm", showing two equal sides. Thus, B matches IV.

• Acute Angle Triangle (C): A triangle where all three interior angles are strictly less than $90^\circ$. Description I gives angles of $70^\circ$, $60^\circ$, and $50^\circ$, all of which are acute. Thus, C matches I.

• Obtuse Angle Triangle (D): A triangle with exactly one angle greater than $90^\circ$. Description II has an angle of $130^\circ$, which is obtuse. Thus, D matches II.

Step 3: Final Answer:
The matching sequence is A-III, B-IV, C-I, D-II, which corresponds to option (D).