NCERT Solutions Class 7 Maths Chapter 14 — Constructions & Tessellations

Solution:

Step 1: The method of constructing a parallel line often involves drawing a transversal and then copying an angle at a different position.

Step 2: If the alternate interior angles formed by a transversal with two lines are equal, then the lines are parallel. This is the geometric principle applied in this construction method.

Solution:

Step 1: After drawing the base segment PQ, the next step is to locate the third vertex R.

Step 2: Vertex R is 3 cm away from Q (QR = 3 cm), so an arc with center Q and radius 3 cm is a valid first arc to draw.

Step 3: Similarly, vertex R is 7 cm away from P (RP = 7 cm), so an arc with center P and radius 7 cm would also be a valid first arc. The intersection of these two arcs will give point R.

Solution:

Step 1: Apply the triangle inequality theorem to each set of side lengths. For a triangle to be formed, the sum of any two sides must be greater than the third side.

Step 2: A) 2 + 2 = 4, which is not > 5. Cannot form a triangle.

Step 3: B) 4 + 5 = 9 > 8; 4 + 8 = 12 > 5; 5 + 8 = 13 > 4. All conditions are met. Can form a triangle.

Step 4: C) 3 + 4 = 7, which is not > 7. Cannot form a triangle.

Step 5: D) 1 + 2 = 3, which is not > 3. Cannot form a triangle.

Solution:

Step 1: The given information is Side-Angle-Side (SAS): AB, ∠B, and BC.

Step 2: First, draw the base segment AB = 6 cm.

Step 3: The included angle is ∠B, which is at point B. Therefore, the next step is to construct an angle of 60° at point B, by drawing a ray BX such that ∠ABX = 60°.

Solution:

Step 1: The acronym SAS stands for Side-Angle-Side.

Step 2: For this criterion to construct a unique triangle, the angle specified must be precisely the one that lies between the two given sides. This is known as the included angle.