Class 8 maths chapter 3 exercise 3.1 solutions

A regular polygon: A polygon having all sides of equal length and the interior angles of equal size is known as regular polygon. (i) 3 sides Polygon having three sides is called a triangle. (ii) 4 sides Polygon having four sides is called a quadrilateral. (iii) 6 sides Polygon having six sides is called a hexagon. In Chapter 3 Understanding Quadrilaterals, we will learn about plane surface and plane figures, different types of polygons like Triangles, Quadrilaterals, Pentagon, Hexagon, Heptagon, etc. Number of diagonals in each polygon, a brief description about CONVEX and CONCAVE polygons. Regular and irregular polygons having 3, 4, 5 and 6. Angle sum property of There are exercises based on the properties of different types of quadrilaterals in this lesson. Just as all the sides and all the angles of the square are equal, the opposite sides of the rectangle are equal, the opposite angle and the diagonal are also equal. Quadrilateral and rectangle have the difference of angles and diagonals. If the diagonals of a

Let ABCD be a parallelogram. Then, AD || BC and AB is a transversal. So, ∠A + ∠B = 180°, [ sum of interior angles on the same side if the transversal is 180°] Similarly, ∠B + ∠C = 1800, ∠C + ∠D = 1800 and ∠D + ∠A = 180°. Thus, the sum of any two adjacent angles of a parallelogram is 180°. Hence, any two adjacent angles of a parallelogram are supplementary. Properties of a Parallelogram Parallelograms are quadrilaterals that have two sets of parallel sides and two sets of congruent sides. A parallelogram’s opposite angles are congruent; its consecutive angles are supplementary; its diagonals bisect each other and its diagonals form two congruent triangles. The diagonals of a parallelogram are equal. The opposite sides and opposite angles of a parallelogram are equal. And these opposite sides and angles make up for two congruent triangles, with the two diagonals being the sides of these two congruent triangles. Hence the diagonals of the parallelogram are equal. Let ABCD be a parallelogram. Draw its diagonals AC. In DABC and DCDA, we have: ∠1 = ∠4 (alternate angles) ∠3 = ∠2 (alternate angles) and AC = CA (common) DABC congruent DCDA (by ASA congruence) AB = CD, BC = DA and ∠B = ∠D. Similarly, by drawing the diagonal BD, we can prove that ∠A = ∠C Thus, AB = CD, BC = DA, B = D and A = C. This proves (i) and (ii). In order to prove (iii) consider parallelogram ABCD and draw its diagonals AC and BD, intersecting each other at O. In triangle OA...

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 – Understanding Quadrilaterals, has been designed by the NCERT to test the knowledge of the student on the following topics : • Introduction • Polygons Classification of polygons Diagonals Convex and concave polygons Regular and irregular polygons Angle sum property NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 1. Given here are some figures. Classify each of them on the basis of the following a) Simple curve b) Simple closed curve c) Polygon d) Convex polygon e) Concave polygon Solution: (a) Simple curves: 1, 2, 5, 6, 7 (b) Simple closed curves: 1, 2, 5, 6, 7 (c) Polygons: 1, 2 (d) Convex polygon: 2 (e) Concave polygon: 1 2. How many diagonals each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle Solution: (a) A convex quadrilateral has 2 diagonals, (b) A regular hexagon has 9 diagonals. (c) A triangle has no diagonals. 3. What is the sum of the measures of angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? Solution: A convex quadrilateral can be divided into two triangle by one of the diagonals ∴ Angle sum of convex quadrilateral = Angle sum of two triangles = 2 × 180° = 360° Similarly, a non-convex quadrilateral can also be divided into two triangles Hence, the property holds true for non-convex quadrilaterals also. 4. Examine the table. (Each figure is divided into t...

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Understanding Quadrilaterals NCERT solutions for class 8 maths chapter 3 exercise 3.2 understanding quadrilaterals is purely based on the exterior angle property which states that the sum of all the exterior angles of a In order to successfully attempt all the problems in this exercise students must have good calculation accuracy. They must also be able to read the question and understand the application of the ☛ Download NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Exercise 3.2 Class 8 Chapter 3 Download PDF More Exercises in Class 8 Maths Chapter 3 • • • NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Formulas • Exterior Angle of a Polygon: The sum of the measures of the external angles of any polygon irrespective of the number of sides is 360°. Download Cuemath NCERT Solutions PDF for free and start learning! NCERT Video Solutions for Class 8 Maths Chapter 3 Exercise 3.2 Video Solutions for Class 8 Maths Chapter 3 Exercise 3.2 Video Solutions for Class 8 Maths Exercise 3.2

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) Figure Side 3 4 5 6 Angle sum 180° 2 × 180° = (4 − 2) × 180° 3 × 180° = (5 − 2) × 180° 4 × 180° = (6 − 2) × 180° What can you say about the angle sum of a convex polygon with number of sides? a) 7 b) 8 c) 10 d) n Shaalaa.com has the CBSE Mathematics Class 8 Maths CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students. Concepts covered in Using NCERT Class 8 Maths solutions Understanding Quadrilaterals exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE Class 8 Maths students prefer NCERT Textbook Solutions to score more in exams. Get the free view of Chapter 3, Understanding Quadrilaterals Class 8 Maths additional questions for Mathematics Class 8 Maths CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.