RBSE Solutions Class 6 Maths Chapter 9 Simple Two Dimensional Shapes Exercise 9.2

Question 1. Identify the triangles in the figures.
Answer: The triangles in the given figures are: (iv), (vi), (vii). These figures clearly show shapes with three sides and three angles. Understanding basic shapes is the foundation of geometry.
In simple words: Look at the pictures and pick out the ones that are actual triangles, which are shapes with three straight sides.

🎯 Exam Tip: Pay close attention to the definition of a triangle: a closed shape with three straight sides and three vertices.

Question 2. Identify each of the following triangles on the basis of angles.
Answer:
(i) This is a **Right-angled triangle** because one of its angles is exactly 90 degrees.
(ii) This is an **Acute-angled triangle** because all three of its angles are less than 90 degrees.
(iii) This is an **Obtuse-angled triangle** because one of its angles is greater than 90 degrees. Each type of triangle has specific angle properties that define it.
In simple words: Look at the angles inside each triangle. If it has a 90-degree angle, it's a right triangle. If all angles are small (less than 90), it's acute. If one angle is big (more than 90), it's obtuse.

🎯 Exam Tip: Remember: a right angle is exactly 90 degrees, an acute angle is less than 90 degrees, and an obtuse angle is more than 90 degrees. One large angle makes an obtuse triangle, one 90-degree angle makes a right triangle, and all angles being less than 90 makes an acute triangle.

Question 3. Identify each of the following triangles on the basis of sides.
Answer: Based on the properties of their sides, triangles can be identified as:
(i) An **Equilateral triangle** has all three sides equal in length.
(ii) A **Scalene triangle** has all three sides of different lengths.
(ii) An **Isosceles triangle** has exactly two sides of equal length. The length of a triangle's sides tells us a lot about its shape and symmetry.
In simple words: Check the length of each side. If all sides are the same, it's equilateral. If two sides are the same, it's isosceles. If all sides are different, it's scalene.

🎯 Exam Tip: Clearly remember the definitions: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different).

Question 4. List the name of each of the triangles formed in each of the following figures.
Answer: The names of the triangles in the given figures are:
(i) In the first figure, the triangles formed are: ∆ABC, ∆DEF, ∆DBF, ∆EFC, ∆ADE.
(ii) In the second figure, the triangles formed are: ∆PTU, ∆STW, ∆VRW, ∆UVQ. Complex figures often contain many simpler shapes, including multiple triangles.
In simple words: Look closely at each big picture and find all the smaller triangles hidden inside it. Name each triangle using the letters at its corners.

🎯 Exam Tip: To avoid missing any triangles, systematically identify them by starting from individual points and tracing paths, or by looking for triangles formed by joining three non-collinear points in the figure.

Question 5. Name the types of following triangles on the basis of given angles
(i) 105°, 46°, 29°
(ii) 60°, 60°, 60°
(iii) 57°, 33°, 90°
Answer: The types of triangles on the basis of angles are:
(i) For angles 105°, 46°, 29°: Since one angle (105°) is greater than 90°, it is an **Obtuse-angled triangle**.
(ii) For angles 60°, 60°, 60°: Since all angles are equal (60°) and less than 90°, it is an **Acute-angled triangle**.
(iii) For angles 57°, 33°, 90°: Since one angle is exactly 90°, it is a **Right-angled triangle**. The sum of angles in any triangle is always 180 degrees, which helps classify them.
In simple words: For each set of angles, see if any angle is bigger than 90 degrees (obtuse), if all are smaller than 90 degrees (acute), or if one is exactly 90 degrees (right).

🎯 Exam Tip: Always check all three angles. If even one angle is obtuse or right, that defines the triangle type. If all are acute, then it is an acute triangle.

Question 6. Name types of following triangles on the basis of given sides
(i) 3.5 cm, 3 cm, 1.8 cm.
(ii) 2.8 cm, 2 cm, 2 cm.
Answer:
(i) For sides 3.5 cm, 3 cm, 1.8 cm: All three side lengths are different. This makes it a **Scalene triangle**.
(ii) For sides 2.8 cm, 2 cm, 2 cm: Two of the side lengths are equal (2 cm and 2 cm). This defines it as an **Isosceles triangle**.
(iii) The example 5.2 = 5.2 = 5.2 means all sides are equal. This represents an **Equilateral triangle**. This type of triangle has all sides and all angles equal.
In simple words: Look at the measurements of the sides. If all are different, it's scalene. If two are the same, it's isosceles. If all three are the same, it's equilateral.

🎯 Exam Tip: Remember that "equi" means equal, so an equilateral triangle has equal sides. "Iso" means same or equal, referring to two equal sides, and "scalene" means unequal.

Question 7. Mark True or false
(i) A triangle has three sides, three vertices and three angles.
(ii) If all the angles of a triangle are less than a right angle, then such triangle is called a right angled triangle.
(iii) A triangle having three unequal sides is called an equilateral triangle.
(iv) A triangle having two equal sides is called an isosceles triangle.
(v) In a triangle, if one angle is obtuse angle and two angles are acute angles, then the triangle is called an obtuse angled triangle.
Answer:
(i) **True**. A triangle is a polygon with three sides, three vertices (corners), and three internal angles.
(ii) **False**. If all angles are less than a right angle (90 degrees), it's called an **acute-angled triangle**, not a right-angled triangle.
(iii) **False**. A triangle with three unequal sides is called a **scalene triangle**. An equilateral triangle has all three sides equal.
(iv) **True**. By definition, an isosceles triangle has at least two sides of equal length.
(v) **True**. If a triangle has one obtuse angle (greater than 90 degrees), it is correctly called an **obtuse-angled triangle**, and the other two angles must necessarily be acute. Understanding these fundamental properties is key to working with triangles in geometry.
In simple words: Read each sentence carefully and decide if it describes a triangle correctly (True) or incorrectly (False) based on what you know about triangles.

🎯 Exam Tip: Make sure you know the exact definitions for different types of triangles and their parts (sides, vertices, angles) to correctly identify true or false statements.