RBSE Solutions Class 6 Maths Chapter 9 Simple Two Dimensional Shapes Important Questions

Question 1. If two intersecting lines are mutually perpendicular, then angle between them will be
(i) 60°
(ii) 45°
(iii) 90°
(iv) 180°
Answer: (iii) 90°
In simple words: When two lines cross each other and form a perfect square corner, the angle between them is always 90 degrees. This special type of crossing is called being perpendicular.

🎯 Exam Tip: Remember that "mutually perpendicular" directly means forming a right angle, which is 90 degrees.

Question 2. Angle whose measurement is more than 90° and less than 180°, called
(i) acute angle
(ii) obtuse angle
(iii) complete angle
(iv) None of these
Answer: (ii) obtuse angle
In simple words: An angle that is wider than a right angle (90°) but not as wide as a straight line (180°) is known as an obtuse angle. It looks like a wide-open mouth.

🎯 Exam Tip: Visualize the different angle types: acute is narrow, right is a perfect corner, obtuse is wide, and straight is a flat line.

Question 3. Figure covered by three unequal sides will be
(i) equilateral triangle
(ii) scalene triangle
(iii) right - angled triangle
(iv) isosceles triangle
Answer: (ii) scalene triangle
In simple words: A triangle where all three sides have different lengths is called a scalene triangle. Because the sides are unequal, its angles will also be different.

🎯 Exam Tip: Recall triangle classification: equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides different).

Question 4. Name of polygon made by five sides, will be
Answer: Pentagon
In simple words: A polygon is a closed shape with straight sides. A shape that has exactly five straight sides is known as a pentagon.

🎯 Exam Tip: Learn the names of polygons based on their number of sides: tri- for 3, quad- for 4, pent- for 5, hex- for 6, etc.

Question 5. After looking an angled figure by a magnifying mirror, we find figure as
(i) bigger angle
(ii) smaller angle
(iii) no. effect on angle
(iv) None of these
Answer: (iii) no. effect on angle
In simple words: A magnifying mirror makes objects appear larger, but it does not change the actual size or measurement of the angle itself. The lines just look longer.

🎯 Exam Tip: Magnification changes the apparent size of an object, but intrinsic properties like angle measures remain unchanged.

Question 1. Fill in the blanks
(i) If angle between two intersecting line is 90°, then those lines are mutually perpendicular.
(ii) If one angle of triangle in 90°, then it is called right angled triangle.
(iii) Figure having four sides called quadrilateral.
(iv) We can find area and perimeter of closed figures.
(v) Inner part of closed figure called interior, corner part of closed figure called boundary. and outer part of closed figure called exterior.
(vi) Figure covered by three or more than three sides called polygon.
(vii) Quadrilateral whose opposite sides and all angles are equal called rectangle.
(viii) Quadrilateral whose all sides and all angles are equal called square.

🎯 Exam Tip: Pay close attention to keywords like "mutually perpendicular," "closed figures," and "unequal sides" to correctly identify the geometric terms.

Question 1. What is acute angle?
Answer: An angle whose measure is less than 90° is called an acute angle. It is a sharp angle, smaller than a right angle.
In simple words: An acute angle is any angle that is smaller than 90 degrees.

🎯 Exam Tip: Visualize acute angles as being "cute" and small, always less than 90 degrees.

Question 2. What is straight angle?
Answer: An angle whose measure is exactly 180° is called a straight angle. It forms a straight line.
In simple words: A straight angle is one that measures exactly 180 degrees, forming a flat line.

🎯 Exam Tip: Remember that a straight angle represents half a full circle, hence 180 degrees.

Question 3. How many right angle can a triangle?
Answer: A triangle can have only one right angle. If it had more than one, the sum of its angles would exceed 180 degrees, which is not possible for a triangle.
In simple words: A triangle can only have one right angle (90 degrees).

🎯 Exam Tip: Always remember that the sum of angles in any triangle is 180 degrees. If you have two right angles, you've already used 180 degrees, leaving no space for a third angle.

Question 4. What is rotation?
Answer: Rotation is the movement of an object in a circular path around a central point. For example, a complete round made by the hand of a watch is called 1 rotation, which covers an angle of 360°, also known as a complete angle.
In simple words: Rotation is when something turns around a point, like a clock hand. One full turn is a 360-degree angle.

🎯 Exam Tip: Think of rotation as turning around a fixed point, measured in degrees, with a full rotation being 360 degrees.

Question 5. Identify the given triangles on the basis of their sides.

Answer:
(a) Isosceles triangle (two sides are equal, 2.5 cm)
(b) Scalene triangle (all three sides are different: 4.4 cm, 3 cm, 2.7 cm)
(c) Equilateral triangle (all three sides are equal, 2.7 cm)
(d) Equilateral triangle (all sides are marked 'a', meaning they are equal)
(e) Scalene triangle (all sides are marked with different letters 'a', 'x', 'y', implying unequal lengths)
(f) Scalene triangle (all sides are marked with different letters 'p', 'q', 'r', implying unequal lengths)
In simple words: We look at the lengths of the sides of each triangle. If two sides are the same, it's isosceles. If all three sides are the same, it's equilateral. If all three sides are different, it's scalene.

🎯 Exam Tip: Always check the side lengths or markings carefully. Even if numbers aren't given, identical letter labels (like 'a') indicate equal lengths.

Question 6. Identify the given triangles on the basis of their angles.

Answer:
(i) Obtuse-angled triangle (one angle is 95°, which is greater than 90°)
(ii) Right-angled triangle (one angle is exactly 90°)
(iii) Obtuse-angled triangle (one angle is 106°, which is greater than 90°)
(iv) Acute-angled triangle (all angles are less than 90°: 82°, 49°, 49°)
(v) Acute-angled triangle (all angles are less than 90°: 60°, 60°, 60°)
(vi) Acute-angled triangle (all angles are less than 90°: 80°, 55°, 45°)
(vii) Right-angled triangle (one angle is exactly 90°)
(viii) Obtuse-angled triangle (one angle is 140°, which is greater than 90°)
In simple words: We look at the angles inside each triangle. If there's a 90-degree angle, it's a right triangle. If there's an angle bigger than 90 degrees, it's an obtuse triangle. If all angles are smaller than 90 degrees, it's an acute triangle.

🎯 Exam Tip: The type of triangle is determined by its largest angle: if the largest is acute, it's an acute triangle; if right, it's a right triangle; if obtuse, it's an obtuse triangle.

Question 7. Name each polygon

Answer:
(a) This figure has 4 sides, so it is a Quadrilateral.
(b) This figure has 3 sides, so it is a Triangle.
(c) This figure has 5 sides, so it is a Pentagon.
(d) This figure has 8 sides, so it is an Octagon.
In simple words: We count the number of straight sides on each shape to give it the correct name. Three sides make a triangle, four make a quadrilateral, five make a pentagon, and eight make an octagon.

🎯 Exam Tip: Counting the number of sides is the direct way to identify a polygon's name. Familiarize yourself with prefixes like "tri-", "quad-", "pent-", "oct-" etc.

Question 8. Identify which of the following figures are polygon. If any of them is not polygon, give reason.

Answer:
(a) No, this is not a polygon because it is an open curve. A polygon must be a closed shape.
(b) Yes, this is a polygon because it is a closed figure made up entirely of straight line segments.
(c) No, this is not a polygon because it is a closed curve that is not made up of line segments (it has a curved edge).
(d) No, this is not a polygon because it is a closed curve that is not made up of line segments (it has a curved edge).
In simple words: Polygons are shapes with only straight sides that are fully closed. If a shape has an opening or any curvy parts, it is not a polygon.

🎯 Exam Tip: Remember the two key rules for polygons: they must be closed figures, and all their sides must be straight line segments.

Question 9. Try to construct triangle with the help of matchsticks. Some of them are shown in figure. Can you construct some more?

Note: Use all available matchsticks. Name the type of triangle in each condition. If you cannot construct triangle then think reason.
Answer:
(a) 3 matchsticks: Yes, it is possible to construct an equilateral triangle, with each side using 1 matchstick. (Sides: 1, 1, 1)
(b) 4 matchsticks: No, it is not possible to construct a triangle. For example, if sides were 1, 1, 2, then \( 1 + 1 = 2 \), which is not greater than the third side, violating the triangle inequality rule.
(c) 5 matchsticks: Yes, it is possible to construct an isosceles triangle. For example, two sides can use 2 matchsticks each and the third side can use 1 matchstick. (Sides: 2, 2, 1)
(d) 6 matchsticks: Yes, it is possible to construct an equilateral triangle. Each side can be made of 2 matchsticks. (Sides: 2, 2, 2)
In simple words: We can make triangles using matchsticks if the sum of any two sides is longer than the third side. If we have 3, 5, or 6 sticks, we can usually make a triangle. With 4 sticks, it's hard to make a proper triangle where all sticks form the sides.

🎯 Exam Tip: The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.