RBSE Solutions Class 6 Maths Chapter 9 Simple Two Dimensional Shapes More Ques

(P. No. 141)

Question 1. Draw three closed and three (RBSESolutions.com) open curves.
Answer: Here are examples of three closed curves and three open curves:
A closed curve starts and ends at the same point without lifting the pen, forming a complete shape. An open curve does not end where it started, or requires lifting the pen.
In simple words: Closed curves make a full loop, like a circle or square. Open curves have ends that don't meet, like a letter 'C' or a line.

🎯 Exam Tip: Remember that a closed curve divides a plane into two parts: inside and outside. An open curve does not.

Question 2. In the given figure, which point lie in (RBSESolutions.com) which part (interior, exterior or boundary) of the curve?
Answer: Let's look at the points in relation to the curve provided:

* **Interior points:** A, D (These points are completely inside the curve.)
* **Exterior points:** C, F, G (These points are completely outside the curve.)
* **Boundary points:** B, E (These points are located directly on the line of the curve.)
A point is interior if it lies inside the boundary, exterior if it lies outside, and on the boundary if it lies exactly on the curve itself.
In simple words: Points A and D are inside the shape. Points B and E are exactly on the edge of the shape. Points C, F, and G are outside the shape.

🎯 Exam Tip: Always clearly state the category (interior, exterior, or boundary) for each point. Visual inspection is usually sufficient for simple curves.

Question 2. If all three sides of a triangle are equal, what can you say about the angles, will they be acute angles?
Answer: Yes, if all three sides of a triangle are equal, it is an equilateral triangle. In an equilateral triangle, all three angles are also equal. Since the sum of angles in a triangle is 180 degrees, each angle will be \( \frac{180}{3} = 60 \) degrees. All angles measuring 60 degrees are acute angles (less than 90 degrees).
In simple words: If all sides of a triangle are the same length, then all its angles are also the same. Each angle will be 60 degrees, and 60 degrees is an acute angle.

🎯 Exam Tip: Remember that "equilateral" means equal sides and "equiangular" means equal angles. In a triangle, these two properties always go together.

Question 3. Make a scalene triangle and write down measures of its angles.
Answer: A scalene triangle is one where all three sides have different lengths, and as a result, all three angles also have different measures. Here is an example of a scalene triangle with its angle measures:
In the scalene triangle above, the angle measures are:
* \( \angle X = 90^\circ \)
* \( \angle Y = 25^\circ \)
* \( \angle Z = 65^\circ \)
The sum of these angles is \( 90^\circ + 25^\circ + 65^\circ = 180^\circ \), which is correct for any triangle. This particular scalene triangle is also a right-angled triangle. Every scalene triangle will have three different angle values.
In simple words: A scalene triangle has all sides of different lengths and all angles of different sizes. For example, a triangle with angles 90 degrees, 65 degrees, and 25 degrees is a scalene triangle.

🎯 Exam Tip: When drawing a scalene triangle, ensure none of its sides appear equal, and no two angles appear equal. Using a protractor can help ensure angle measurements are distinct.

Question 4. Do you think it is possible to sketch a triangle (RBSESolutions.com) with two right angles? If yes, sketch it in your notebook. If no, explain the reason.
Answer: No, it is not possible to sketch a triangle with two right angles. The reason is that the sum of all three angles in any triangle must always be exactly 180 degrees. If a triangle were to have two right angles, the sum of just those two angles would be \( 90^\circ + 90^\circ = 180^\circ \). This would leave 0 degrees for the third angle, which is impossible for a closed, three-sided figure. Therefore, a third vertex cannot be formed to close the triangle.
In simple words: No, a triangle cannot have two angles that are both 90 degrees. This is because all angles in a triangle must add up to 180 degrees, and two 90-degree angles already make 180 degrees, leaving no space for a third angle.

🎯 Exam Tip: Always remember the fundamental property of triangles: the sum of interior angles is 180 degrees. This rule helps determine if certain angle combinations are possible.

Text Book Questions (P. No. 139)

Question 1. In which of the following curves, the rat will (RBSESolutions.com) be able to find its way out?
Answer: The rat will be able to find its way out from the curves that are open. An open curve has a starting point and an ending point that are not the same, creating a path through which something can enter or exit. Based on typical illustrations for such a question, these would be the open curves among the given options.
The rat can escape from the following curves (based on common representations of these types of questions):
* (i) An irregular open curve.
* (iv) A curve shaped like a stretched 'S'.
* (v) A curve resembling a heart with an opening.
* (vi) A curve resembling an irregular blob with an opening.
* (vii) A curve resembling a simple line segment.
* (viii) A curve resembling an inverted 'U'.
The key feature is that these curves do not form a complete loop, allowing an exit. If a curve is closed, the rat would be trapped inside.
In simple words: The rat can get out of any curve that is not fully closed. These are like paths with an entrance and an exit.

🎯 Exam Tip: To identify an open curve, imagine tracing it with a pencil. If you can complete the trace without lifting your pencil and without returning to the exact starting point (or if the path simply has clear start and end points), it's an open curve.

(P. No. 140)

Question 1. Can you tell which type of curve, the (RBSESolutions.com) letter p is?
Answer: The letter 'p' is an open curve. While part of the letter forms a closed loop (the circular part), the overall curve that makes the entire letter 'p' (including its vertical stem) is not completely closed. You cannot trace the entire letter 'p' starting and ending at the same point without lifting your pen. Although it contains a closed loop, the complete shape does not allow a continuous return to the starting point.
In simple words: The letter 'p' is an open curve. You cannot draw it in one continuous line without lifting your pen and ending exactly where you started.

🎯 Exam Tip: Even if a curve contains closed segments, if the overall shape does not allow you to return to the starting point without lifting your drawing tool, it is considered an open curve.

(P. No. 143)

Question 1. (A geoboard consists of a physical board with a certain number of nails half driven in it.) See the polygon made on the geoboard. How many sides does the polygon have? Try to make as many polygons as you can, of different number of sides.
Answer: The polygon shown on the geoboard in the figure is an octagon, which means it has 8 sides. A geoboard is a great tool for understanding polygons because you can easily form shapes using rubber bands around the nails. You can make many different polygons with varying numbers of sides on a geoboard.
Here are examples of other polygons you can make:
* **Triangle:** 3 sides
* **Quadrilateral:** 4 sides (e.g., square, rectangle, rhombus)
* **Pentagon:** 5 sides
* **Hexagon:** 6 sides
* **Heptagon:** 7 sides
* **Decagon:** 10 sides
The number of sides a polygon has determines its name.
In simple words: The shape shown on the geoboard has 8 sides, so it is an octagon. You can use a geoboard to make many shapes, like triangles (3 sides), squares (4 sides), and pentagons (5 sides).

🎯 Exam Tip: Knowing the names of polygons based on their number of sides (e.g., triangle for 3, quadrilateral for 4, pentagon for 5, hexagon for 6) is a key concept in geometry.

Question 2. Identify the triangles in the following figures.
Answer: Triangles are geometric shapes that have three sides and three corners (vertices). In the given figures, we need to look for objects that fit this description.
The figures show several everyday objects, and the parts that represent triangles are:
* The **road sign** (often shaped like an equilateral or isosceles triangle).
* The **roof of the house** (typically forms a triangle).
* The **flag** attached to the pole (the fabric itself forms a triangular shape).
These objects clearly display the three-sided, three-cornered characteristic of a triangle. The hanger and the full house structure (excluding the roof) are not triangles.
In simple words: Look for shapes with exactly three straight sides and three corners. In the pictures, the road sign, the house roof, and the flag are all examples of triangles.

🎯 Exam Tip: When identifying shapes, count the number of sides and corners carefully. This is the most reliable way to classify basic geometric figures.

(P. No. 148)

Question 1. Identify all the quadrilaterals (RBSESolutions.com) in the following figures.
Answer: Quadrilaterals are geometric shapes that have exactly four sides and four corners (vertices). In the provided figures, we need to find the objects that demonstrate this four-sided property.
Based on the figures, the quadrilaterals are:
* The **grid pattern** (formed by many small squares or rectangles, which are quadrilaterals).
* The **tabletop** (a rectangular shape, which is a type of quadrilateral).
* The **kite** (a traditional kite shape is a quadrilateral).
These objects are all examples of quadrilaterals, as they all possess four distinct sides and four vertices. Recognizing these shapes in everyday objects helps to understand geometry better.
In simple words: Quadrilaterals are shapes with four straight sides. The grid, the table, and the kite are all quadrilaterals because they have four sides.

🎯 Exam Tip: Remember that squares and rectangles are specific types of quadrilaterals, but any four-sided closed figure is a quadrilateral.

Question 2. Look at the following quadrilateral ABCD and conclude :
1. How many sides does it have?
2. How many vertices does it have?
3. How many angles does it have?
Answer: Let's analyze the quadrilateral ABCD:
1. **Sides:** A quadrilateral has 4 sides. In this figure, the sides are AB, BC, CD, and DA.
2. **Vertices:** A quadrilateral has 4 vertices (corners). The vertices are A, B, C, and D.
3. **Angles:** A quadrilateral has 4 interior angles. The angles are \( \angle A \), \( \angle B \), \( \angle C \), and \( \angle D \).
A quadrilateral is defined by these four elements: four straight line segments (sides), four points where the sides meet (vertices), and four angles formed at these vertices. This is a fundamental definition in geometry.
In simple words: A quadrilateral is a shape that always has 4 sides, 4 corners (called vertices), and 4 angles. For the shape ABCD, the sides are AB, BC, CD, DA. The corners are A, B, C, D. The angles are the spaces inside at each corner.

🎯 Exam Tip: Always state the exact number of sides, vertices, and angles for a quadrilateral, and if asked, list them using the correct notation (e.g., \( \angle A \) for an angle, AB for a side).