NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.1) Exercise 3.1
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When you draw a few dots on a plane surface and connect them without raising your hand or retracing your steps, the resulting figure is called a plane curve. You have already studied the different types of plane curves(Simple closed, closed curve, Simple curve, etc.) in earlier classes.
By definition, a polygon is a simple closed curve made up of only line segments. Some common examples of polygons are square, rectangle, square, etc.
Based on the number of sides in a polygon, it can be classified into different shapes. A three-sided polygon is called a triangle, four-sided is called quadrilateral, and so forth. Read the below definition, they will come handy in ex 3.1 Class 8 NCERT Solutions.
Diagonals - A line segment that joins two non-consecutive (occurring one after the other) vertices in a polygon is called a diagonal.
Interior & Exterior - The area enclosed in the boundary of the polygon is called interior while the area outside is called exterior.
Concave Polygon and Convex polygon - All the diagonals lie in the interior of a concave polygon and no two line segments join the same vertices, whereas in convex polygon a diagonal can lie in both the interior and exterior portion of the polygon and more than one line segments can meet at one vertex.
A polygon is a regular polygon when it has the following features:
A square and equilateral triangle both are regular polygons. On the other hand, a rectangle is not, because all the angles are equal to one another(90 °) but the length of all sides is not the same. Such a polygon is called an irregular polygon. If you understand the difference, you wouldn’t need exercise 3.1 Class 8 NCERT Solutions for comparison questions.
The angle sum property of a triangle states that the sum of all the three angles is equal to 180°. You will apply it in a number of questions in Exercise 3.1.
If you are looking for NCERT Solutions for Class 8 Maths Chapter 3 exercise 3.1, the below hints will certainly help you.
Question 1. In the first question you are asked to classify the figure into the given options.
(a)Simple Curve -It is a type of curve that doesn’t cross itself. Figure(1) is a simple curve because it doesn’t close itself. Hence, it is a simple curve. In this way you can compare the rest of the figures and find which figure can be classified under which option. If you need NCERT Math book Class 8 exercise 3.1 solution along with complete explanations, Vedantu has it all.
You are asked the number of diagonals the quadrilaterals have. The first option is (a)Convex Quadrilateral - Since, diagonals lie in the interior of a convex quadrilateral, and no line segment can join two different points, it will have two diagonals. Similarly, you can solve the rest of the parts of the question of Class 8 Maths Chapter 3 exercise 3.1. If you are finding it difficult to figure out the solution of NCERT Maths Cass 8 exercise 3.1, you can contact our experts.
The question asks you to define the sum of angles in a convex quadrilateral. Let ABCD be a convex quadrilateral and AC be diagonal. As you can see AC divides the quadrilateral into two triangles. According to the angle sum property, the sum of all angles in a triangle is 180. Thus, the sum of all the angle in △ ABC =△ ADC = 180°. After adding all the angles formed by both the triangle you will find the measure of a convex quadrilateral.
For non-convex quadrilateral, checkout Vedantu ex 3.1 Class 8 free pdf. It has covered the solution to our questions in the exercise.
As you can see from the table, the sum of the angles in a polygon with n sides = (n-2 )X 180 °. Applying this formula you can easily solve all the option in the question. For your convenience, we have explained part (a) below.
For (a) n = 7
Therefore, the sum of the angles will be (7-2) x 180 ° = 5 X 180 ° = 900 °. Still in doubt? Review our NCERT Maths Class 8 Chapter 3 exercise 3.1 solutions. The step-by-step solution along with the simple explanations make learning math a joyride.
Regular polygon - You are already familiar with it. It is a polygon which is both equilateral and equiangular.
(i) Think about a polygon having three sides of equal length and equal angle.
Find it hard to solve NCERT Maths Class 8 Chapter 3 exercise 3.1? Read the solutions from our experts.
The addition of all the interior angles in a quadrilateral is 360°. So, to find the value of ‘x’ in the question, you have to subtract the sum of all the remaining angles from 360° to find the value of x.
(a)Here 50°+360°+120°+x = 180° Solving this equation further, you will find the solution to this part. Use the same approach to solve (b),(c), and (d). Find it hard? Get a detailed explanation of exercise 3.1 Class 8 NCERT Solutions from our tutors.
Here we have to use three concepts, the angle sum property, exterior angle theorem and linear pair.
Angle sum property -We have already discussed the angle sum property a couple of times above.
Exterior angle theorem - The measure of an exterior angle is the sum of the adjacent angle and an interior angle opposite to it.
Linear pair - When two adjacent angles make a single line, their sum = 180°, and they are called linear pair.
Download NCERT Maths Class 8 to help you to revise complete syllabus ans score more marks in your examinations.
Every student wants to brush up his mathematics and score top grades in his exams. At times, it can become a challenge to find the right answers. The students are introduced to the various aspects of a polygon(diagonal, interior, and exterior). Our NCERT Solutions for Class 8 Maths Chapter 3 is written by the subject matter experts. Most pupils who are weak in math lag behind because they still haven’t gotten the grasp of basics. The ex 3.1 Class 8 ‘Understanding quadrilaterals’ tests student’s knowledge of polygons and their classification. We provide free chapter-wise solution and study material to help students in their self-study. If you are more comfortable with video lesson, you can view Understanding quadrilaterals exercise 3.1. Everything you read in the understanding quadrilaterals Class 8 exercise 3.1 study materials are chosen and put together by our experts. For improving student's academic performance we have created study courses that they can pace as per their preference.
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