Class 7 Maths - KARNATAKA
Constructions and Tilings
In the chapter 'Constructions and Tilings', Karnataka Class 7 students learn the practical art of geometry using tools like a ruler, compass, protractor, and set-squares. You will learn how to construct parallel lines, perpendicular lines, and various types of triangles with precision. The second part introduces the fascinating world of tilings, or tessellations, exploring how shapes can fit together perfectly without gaps or overlaps to cover a flat surface. This chapter is vital for board exams as it tests your drawing accuracy, logical thinking, and spatial reasoning skills through both short answers and step-by-step construction problems.
Start Learning FreeKey Concepts
Construction of Parallel Lines
Drawing a line parallel to a given line through an external point using the alternate interior angles or corresponding angles property.
Construction of Perpendicular Lines
Drawing a line at a 90-degree angle to a given line, either from a point on the line or from a point outside the line using a compass and ruler.
Construction of Triangles
Drawing triangles accurately when different combinations of sides and angles are given, such as SSS, SAS, ASA, and RHS criteria.
Tessellations and Tilings
Covering a 2D plane using one or more geometric shapes (tiles) with no overlaps and no gaps between them.
Condition for Regular Tiling
A regular polygon can tile a plane only if its interior angle divides 360 degrees completely without leaving a remainder.
Important Formulas
Board Exam Info
In Karnataka (KSEEB) Class 7 mathematics examinations, this chapter typically carries around 6 to 8 marks. Common question types include step-by-step geometrical construction problems of lines and triangles, identifying whether a given shape can tile a surface, and short conceptual questions on tessellations.
Frequently Asked Questions
Why do my construction lines not meet properly in triangles?
This usually happens if your pencil is not sharp, your compass slips, or you misread measurements on your ruler. Always use a sharply pointed pencil and hold the compass firmly from the top.
Can any polygon form a tiling?
No, only polygons whose interior angles add up to 360 degrees around a single vertex can tile a plane. Triangles, squares, and regular hexagons can tile, but pentagons cannot tile by themselves.
Do I need to write the steps of construction in the exam?
Yes, for construction questions, writing brief, numbered steps of construction alongside your final diagram is usually required to get full marks.
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