GSEB Class 6 Maths Solutions Chapter 4 ભૂમિતિના પાયાના ખ્યાલો Exercise 4.4

Question 1. Draw a rough sketch of \( \Delta \text{ABC} \). Mark point P in its interior and point Q in its exterior. Is point A in its interior or exterior?
Answer: Here, \( \Delta \text{ABC} \) is displayed. Observe that point P is located within the interior of \( \Delta \text{ABC} \). Point Q is situated outside the exterior region of \( \Delta \text{ABC} \). Point A functions as a vertex of \( \Delta \text{ABC} \), therefore, point A is not positioned either inside or outside \( \Delta \text{ABC} \). It is specifically a point lying on \( \Delta \text{ABC} \).
In simple words: First, draw a triangle and label its corners A, B, C. Place one dot, P, inside the triangle, and another dot, Q, outside it. Point A itself is a corner of the triangle, so it's not inside or outside; it's right on the edge.

Exam Tip: When dealing with geometric figures, clearly label all points as specified in the question. Distinguish between points in the interior, exterior, and on the boundary of a shape.

 

Question 2. Write the answers to the questions given based on the figure drawn below:
(a) What are the three triangles in the figure?
(b) Write the names of seven angles.
(c) Write the names of six line segments.
(d) Which two triangles share vertex B?

Answer:
(a) The drawing above displays three triangles:
1. \( \Delta \text{ABC} \)
2. \( \Delta \text{ABD} \)
3. \( \Delta \text{ADC} \)
(b) The seven angles created in the given drawing are:
1. \( \angle B \)
2. \( \angle C \)
3. \( \angle BAC \)
4. \( \angle BAD \)
5. \( \angle CAD \)
6. \( \angle ADB \)
7. \( \angle ADC \)
(c) The six line segments found in the drawing above are:
1. \( \overline{\mathrm{AB}} \)
2. \( \overline{\mathrm{AC}} \)
3. \( \overline{\mathrm{BC}} \)
4. \( \overline{\mathrm{AD}} \)
5. \( \overline{\mathrm{BD}} \)
6. \( \overline{\mathrm{DC}} \)
(d) The two triangles that possess vertex B in common are \( \Delta \text{ABC} \) and \( \Delta \text{ABD} \).
In simple words: (a) Look for all the three-sided shapes: the big one, and the two smaller ones inside it. (b) Count all the corners where lines meet and name them properly. (c) Find all the straight lines that connect two points. (d) Identify the triangles that both have the point B as one of their corners.

Exam Tip: Always carefully examine the provided figure to correctly identify all geometric elements like triangles, angles, and line segments. Pay attention to labels and common parts between different shapes.