NCERT MCQ Solutions for Class 5 Maths Mela Chapter 7 Shapes and Patterns

According to the weaving instructions, the basic mat pattern starts with Row 1 going 1 under and 1 over repeatedly, while Row 2 alternates with 1 over and 1 under. This creates the fundamental alternating weave pattern that gives the mat its structure and appearance.

Regular pentagons do not tessellate because when you try to fit them together around a point or fill a region, gaps are left between the shapes. This happens because the interior angles of regular pentcte a seamless tiling pattern.

Six equilateral triangles can fit perfectly around a point without any gaps or overlaps. Each equilateral triangle has interior angles of 60 degrees, and 6 times 60 equals 360 degrees, which is exactly what is needed to fill the space around a point completely.

Regular hexagons tessellate perfectly because their interior angles are 120 degrees, and three hexagons meeting at a point create exactly 360 degrees with no gaps or overlaps. This is why hexagonal patterns are common in nature, like in honeycomb structures created by bees.

An isosceles triangle is defined as having exactly two equal sides and consequently two equal angles. The equal angles are opposite to the equal sides. This is different from an equilateral triangle which has all three sides equal, and a scalene triangle which has no equal sides.

A scalene triangle is one where all three sides have different lengths and all three angles are different. This is the most general type of triangle, as opposed to equilateral triangles where all sides are equal, or isosceles triangles where two sides are equal.

In a kite shape, there are two pairs of adjacent equal sides. For example, if we label the sides as 1, 2, 3, 4 going around, then side 1 equals side 2, and side 3 equals side 4. The adjacent sides meet at a vertex, unlike in parallelograms where opposite sides are equal.

A parallelogram is defined as a quadrilateral where opposite sides are parallel and equal in length. Additionally, opposite angles in a parallelogram are equal. This property distinguishes it from other quadrilaterals like kites where adjacent sides are equal instead of opposite sides.

A rectangle is a special type of parallelogram where all four angles are right angles measuring 90 degrees each. While maintaining the parallelogram property of having opposite sides equal and parallel, the right angles give rectangles their distinctive rectangular shape and make them particularly useful in construction and design.

When you draw any two diameters of a circle and connect their four endpoints, you always get a rectangle. This happens because the diameters pass through the center and create equal distances from the center to each endpoint, and the angles formed are always right angles due to the geometric properties of circles.

When a 3x3x3 cube made of 27 small cubes is painted on all exterior faces, only the 8 corner cubes have three faces painted. These corner cubes are located at the vertices of the large cube, where three faces of the large cube meet, so three faces of each corner cube get painted.

The pattern involves connecting points that are 10 positions apart around the circle. You start at point 1, go to point 11 (which is 10 positions away), then to point 2, then to point 12, and so on. This creates a star-like geometric pattern within the circle.

An icosahedron is made up entirely of triangular faces. The prefix “icosa” means twenty, so an icosahedron has 20 triangular faces. All these triangular faces are equilateral triangles that are identical in size and shape, making the icosahedron one of the five regular polyhedra.

The “2 over, 1 under” pattern represents a more complex weaving design compared to the basic “1 over, 1 under” alternating pattern. This creates a different visual texture and requires following specific rules for each row to maintain the pattern consistency throughout the woven mat.

Regular squares fit perfectly around a point with exactly 4 squares meeting at each vertex. Since each interior angle of a square is 90 degrees, four squares create 4 x 90 = 360 degrees around a point, with no gaps or overlaps, which is why square tiles are commonly used in flooring.

When you cut an equilateral triangle in half along its height (altitude), you create two congruent isosceles triangles. Each new triangle has two equal sides, one being half of the original base and the other being the altitude of the original triangle, making them isosceles by definition.

Using triangular pieces from a divided rhombus, you can create various quadrilaterals including kites, parallelograms, and rectangles. The document specifically mentions that you can make different types of 4-sided shapes, with examples showing kites and parallelograms as distinct possibilities along with other quadrilateral forms.

In a traditional tangram set, all the pieces are cut from a square and maintain consistent angular relationships. The shapes typically include angles of 45, 90, and sometimes 135 degrees, which allows them to fit together in various combinations while maintaining geometric harmony throughout different arrangements.

Adjacent sides in a quadrilateral are sides that share a common vertex or corner, meaning they touch each other at their endpoints. Opposite sides are across from each other and do not share a vertex. This distinction is crucial for understanding properties of different quadrilaterals like kites versus parallelograms.

For a proper tessellation pattern to work with multiple shapes, the same combination of shapes must meet at each vertex point throughout the pattern. This ensures regularity and allows the pattern to continue infinitely without disruption. The angles of the shapes meeting at each point must also sum to exactly 360 degrees.