Question

Identify the correct geometric definitions related to quadrilaterals and triangles from the following statements:
A. A figure with four equal angles and equal opposite sides is an 'Ayata' (Rectangle).
B. The sum of three angles of a triangle is less than two right angles.
C. A triangle with one angle equal to 90 degrees is a 'Sama-konam' (Right triangle).
D. A figure with all four sides equal and all four angles equal is a 'Samachatur-bhuja' (Square).
E. A triangle is defined as having exactly 5 primary components.

• A. Only A, B, C
• B. Only B, C, D
• C. Only A, B, D
• D. Only D, C, A

Hint:

Ignore B and E immediately. A triangle's angles always sum to 180, and a triangle is defined by its 3 sides and 3 angles ($3+3=6$). This makes any option containing B or E wrong.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Indian geometry (Ganita-pada) provides precise definitions for various shapes. These definitions are used to calculate areas, perimeters, and diagonal lengths for sacrificial altars (Vedi) and astronomical constructions.

Step 2: Detailed Explanation of Statements:
1. Ayata (A): In Sanskrit math, 'Ayata' refers to a rectangle. The definition provided—equal opposite sides and all four angles equal (to 90 degrees)—is the classical definition. Statement (A) is TRUE.
2. Triangle Angles (B): As established in basic geometry, the sum of the angles of a triangle is exactly $180^\circ$ (two right angles), not less. Statement (B) is FALSE.
3. Right Triangle (C): A triangle containing one right angle ($90^\circ$) is called a 'Sama-kona' or 'Kona-tribhuja'. Statement (C) is TRUE.
4. Square (D): 'Samachatur-bhuja' literally means "equal four arms." When combined with equal angles, it defines a square. Statement (D) is TRUE.
5. Triangle Components (E): As per Question 29, a triangle has 6 components (3 sides and 3 angles), not 5. Statement (E) is FALSE.

Step 3: Verification with Options:
- True statements are A, C, and D.
- Option (4) presents this set: "Kevalam D, C, A".

Step 4: Final Answer:
The correct set of geometric definitions is A, C, and D.