GSEB Class 6 Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.5

Gujarat Board Textbook Solutions Class 6 Math Chapter 4 Basic Geometrical Ideas Ex 4.5

Question 1. Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
Answer:
(i) The drawing shows a quadrilateral named PQRS.(ii) Its diagonals are \( \overline{PR} \) and \( \overline{QS} \).
(iii) The place where these diagonals meet, labeled O, is inside the quadrilateral.

Exam Tip: When drawing a quadrilateral, ensure all four vertices are distinct and connected in sequence. The diagonals must connect opposite vertices.

Question 2. Draw a rough sketch of a quadrilateral KLMN State:
(a) two pairs of opposite sides,
(b) two pairs of opposite angles,
(c) two pairs of adjacent sides,
(d) two pairs of adjacent angles.
Answer:(a) The pairs of opposite sides are \( \overline{KL} \) and \( \overline{MN} \), and also \( \overline{LM} \) and \( \overline{NK} \).
(b) The pairs of opposite angles are \( \angle K \) and \( \angle M \), and also \( \angle L \) and \( \angle N \).
(c) The two pairs of adjacent sides are \( \overline{KL} \) and \( \overline{LM} \), and \( \overline{MN} \) and \( \overline{NK} \). Other valid pairs include \( \overline{LM} \) and \( \overline{MN} \), and \( \overline{NK} \) and \( \overline{KL} \).
(d) The two pairs of adjacent angles are \( \angle K \) and \( \angle L \), and \( \angle L \) and \( \angle M \). Other valid pairs include \( \angle M \) and \( \angle N \), and \( \angle N \) and \( \angle K \).

Exam Tip: Remember that opposite parts do not share a common vertex or side, while adjacent parts always share one. Drawing a quick sketch helps to visualize and correctly identify these parts.

Question 3. Investigate: Use strips and fasteners to make a triangle and a quadrilateral. Try to push inward at any one vertex of the triangle. Do the same for the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid? Why is it that structures like electronic towers make use of triangular shapes and not quadrilaterals?
Answer: When you try to push inward at a vertex of the triangle, you will find that the triangle does not change its shape easily. It remains firm and fixed. However, when you do the same with a quadrilateral, it will easily distort or change its shape, becoming flatter or collapsing. This means the triangle is rigid, while the quadrilateral is not.
Triangles are inherently stable geometric shapes because their angles are fixed once the side lengths are set. A triangle cannot change its angles without changing the length of one of its sides. Quadrilaterals, on the other hand, can easily change their angles and shape without altering the lengths of their sides. This property of rigidity makes triangles much stronger and more stable for construction.
Because of this strength, structures like electronic towers, bridges, and roofs use triangular shapes extensively. The use of triangles ensures that these structures are stable and can withstand external forces without collapsing or bending. If quadrilaterals were used instead, the structures would be unstable and prone to deformation, making them unsafe and less durable.
In simple words: When you push on a triangle made of strips, it holds its shape. When you push on a quadrilateral, it easily changes shape. Triangles are strong and rigid, which is why tall structures like towers use them to stay firm and not bend. Quadrilaterals are not as strong and can be pushed out of shape easily.

Exam Tip: Understanding the rigidity of triangles is key in engineering and architecture. Always explain how fixed side lengths lead to fixed angles in triangles, making them ideal for stable structures.