# NCERT Class 7 Mathematics Chapter 14 Constructions and Tilings: Summary, Concepts, and Revision Notes | SwaVid This chapter introduces fundamental geometric constructions using only a ruler and compass, building upon concepts learned in Class VI. It covers the co... Canonical: https://swavid.com/maths/class/7/chapter/constructions-and-tilings Source: https://swavid.com/maths/class/7/chapter/constructions-and-tilings # Constructions and Tilings ## Concepts in this chapter ## The ideas this chapter keeps returning to ## Where this chapter usually trips people up ## Find the gaps before this chapter finds them for you. ## Related chapters ### Construction of a Line Parallel to a Given Line Chapter 14 · Class 7 Mathematics This chapter introduces fundamental geometric constructions using only a ruler and compass, building upon concepts learned in Class VI. It covers the construction of parallel lines and various types of triangles based on specific criteria. Additionally, the chapter explores the fascinating concept of tilings, also known as tessellations, explaining how different shapes can fit together without gaps or overlaps to cover a surface. Your study route Key topics This section teaches how to construct a line parallel to a given line 'l' passing through a point 'P' not on 'l'. The method involves drawing a transversal through P, copying an angle (corresponding angles or alternate interior angles) at point P to create the parallel line. Example Example 1: Construct a line parallel to a given line l through a point P not on l. Watch out Students might confuse corresponding angles with alternate interior angles or struggle with accurately copying an angle using a compass. This section teaches how to construct a line parallel to a given line 'l' passing through a point 'P' not on 'l'. The method involves drawing a transversal through P, copying an angle (corresponding angles or alternate interior angles) at point P to create the parallel line. Tap the card for an example Example Example 1: Construct a line parallel to a given line l through a point P not on l. Why it matters Parallel lines are fundamental in geometry and are used in architecture, engineering, and design. Understanding their construction helps in visualizing and creating structures with parallel components. Watch out Students might confuse corresponding angles with alternate interior angles or struggle with accurately copying an angle using a compass. Ask at home Ask the child to demonstrate constructing a parallel line to a line you draw on paper, passing through a specific point. Check if they use a compass and ruler correctly and explain the steps. This chapter delves into essential geometric constructions, starting with the method to draw a line parallel to a given line through an external point using a ruler and compass. It then systematically covers the construction of triangles based on four congruence criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and RHS (Right-angle-Hypotenuse-Side). For each criterion, clear step-by-step procedures are provided with illustrative examples. The latter part of the chapter introduces the concept of tilings or tessellations, explaining how shapes can cover a plane without gaps or overlaps. It discusses which regular polygons can tile a plane based on their interior angles and briefly touches upon semi-regular tilings, fostering an understanding of geometric patterns in everyday life. Chapter summary This chapter delves into essential geometric constructions, starting with the method to draw a line parallel to a given line through an external point using a ruler and compass. It then systematically covers the construction of triangles based on four congruence criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and RHS (Right-angle-Hypotenuse-Side). For each criterion, clear step-by-step procedures are provided with illustrative examples. The latter part of the chapter introduces the concept of tilings or tessellations, explaining how shapes can cover a plane without gaps or overlaps. It discusses which regular polygons can tile a plane based on their interior angles and briefly touches upon semi-regular tilings, fostering an understanding of geometric patterns in everyday life. What you should learn Keep these close A line parallel to a given line can be constructed by copying an angle (corresponding or alternate interior) at an external point. A unique triangle can be constructed if specific measurements are provided. SSS criterion: Three side lengths uniquely define a triangle. SAS criterion: Two side lengths and the included angle uniquely define a triangle. ASA criterion: Two angles and the included side length uniquely define a triangle. RHS criterion: For a right-angled triangle, the hypotenuse and one leg uniquely define it. Always start with a rough sketch before beginning a construction. Use a sharp pencil, ruler, and compass for accurate constructions. Tiling (tessellation) is covering a plane with shapes without gaps or overlaps. For a regular polygon to tile a plane by itself, its interior angle must be a divisor of 360 degrees. Equilateral triangles, squares, and regular hexagons are regular polygons that can tile a plane. Regular pentagons and octagons cannot tile a plane by themselves because their interior angles are not divisors of 360 degrees. Common confusions It is easy to think Thinking that any three lengths can form a triangle. The clearer idea The sum of the lengths of any two sides of a triangle must be greater than the length of the third side (triangle inequality). If this condition is not met, a triangle cannot be constructed. It is easy to think Confusing the 'included angle' in SAS or 'included side' in ASA. The clearer idea In SAS, the angle must be between the two given sides. In ASA, the side must be between the two given angles. Always refer to the vertices involved. It is easy to think Believing that all polygons can tile a plane. The clearer idea Only specific polygons, particularly those whose interior angles are factors of 360 degrees (for regular polygons), can tile a plane without gaps or overlaps. It is easy to think Not drawing a rough sketch before starting the construction. The clearer idea A rough sketch helps visualize the final figure, plan the steps, and correctly label vertices and measurements, reducing errors during the actual construction. Before you push ahead Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns. Keep exploring Class 7 Source - Construct a line parallel to a given line through a point not on the line. - Construct triangles accurately given three side lengths (SSS criterion). - Construct triangles accurately given two side lengths and the included angle (SAS criterion). - Construct triangles accurately given two angles and the included side (ASA criterion). - Construct right-angled triangles given the hypotenuse and one leg (RHS criterion). - Understand the concept of tiling and identify which regular polygons can tile a plane. - Construct a line parallel to a given line through a point not on the line. - Construct triangles accurately given three side lengths (SSS criterion). - Construct triangles accurately given two side lengths and the included angle (SAS criterion). - Construct triangles accurately given two angles and the included side (ASA criterion). - Construct right-angled triangles given the hypotenuse and one leg (RHS criterion). - Understand the concept of tiling and identify which regular polygons can tile a plane. - NCERT Class 7 Mathematics textbook: Ganita Prakash-II : Chapter 14: Constructions and Tilings ## Key Links - [NCERT Mathematics](https://swavid.com/maths) - [Class 7](https://swavid.com/maths/class/7) - [Start with concepts](https://swavid.com/maths/class/7/chapter/constructions-and-tilings) - [Check a prerequisite](https://swavid.com/learning-debt-identifier) - [Concepts](https://swavid.com/maths/class/7/chapter/constructions-and-tilings) - [Practice](https://swavid.com/maths/class/7/chapter/constructions-and-tilings/practice-questions) - [NCERT Solutions](https://swavid.com/maths/class/7/chapter/constructions-and-tilings/ncert-solutions) - [Find the gaps before this chapter](https://swavid.com/learning-debt-identifier) - [Learn this chapter adapted to you](https://swavid.com/learning-style-test) - [Previous chapter 13 . Connecting the Dots](https://swavid.com/maths/class/7/chapter/connecting-the-dots) - [Next chapter 15 . Finding the Unknown](https://swavid.com/maths/class/7/chapter/finding-the-unknown) - [All Class 7 chapters](https://swavid.com/maths/class/7) - [13 Connecting the Dots Revisiting Bar Graphs · Introduction to Double Bar Graphs Open chapter](https://swavid.com/maths/class/7/chapter/connecting-the-dots) - [15 Finding the Unknown What is an Equation? · Setting up an Equation from Statements Open chapter](https://swavid.com/maths/class/7/chapter/finding-the-unknown) - [12 Another Peek Beyond the Point Introduction to Exponents · Laws of Exponents (Product and Quotient) Open chapter](https://swavid.com/maths/class/7/chapter/another-peek-beyond-the-point) - [NCERT Class 7 Mathematics textbook: Ganita Prakash-II](https://ncert.nic.in/textbook/pdf/gegp206.pdf)