{"id":29320,"date":"2021-12-30T17:52:35","date_gmt":"2021-12-30T12:22:35","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=29320"},"modified":"2024-09-05T14:23:25","modified_gmt":"2024-09-05T08:53:25","slug":"extra-questions-class-8-maths-chapter-3-understanding-quadrilaterals","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/class-8\/maths\/understanding-quadrilaterals-extra-questions-maths-chapter-3\/","title":{"rendered":"Extra Questions &#8211; Class 8 Maths Chapter 3 Understanding Quadrilaterals"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/class-8\/maths\/understanding-quadrilaterals-extra-questions-maths-chapter-3\/#Class_8_Maths_Chapter_3_Extra_Questions_with_Solutions_-_Understanding_Quadrilaterals\" title=\"Class 8 Maths Chapter 3 Extra Questions with Solutions &#8211; Understanding Quadrilaterals\">Class 8 Maths Chapter 3 Extra Questions with Solutions &#8211; Understanding Quadrilaterals<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/class-8\/maths\/understanding-quadrilaterals-extra-questions-maths-chapter-3\/#Very_Short_Answer_Type\" title=\" Very Short Answer Type\"> Very Short Answer Type<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/class-8\/maths\/understanding-quadrilaterals-extra-questions-maths-chapter-3\/#Short_Answer_Type\" title=\"Short Answer Type\">Short Answer Type<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/class-8\/maths\/understanding-quadrilaterals-extra-questions-maths-chapter-3\/#Higher_Order_Thinking_Skills_HOTS\" title=\"Higher Order Thinking Skills (HOTS)\">Higher Order Thinking Skills (HOTS)<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>In <strong>Class 8 Mathematics, Chapter 3 focuses on Understanding Quadrilaterals<\/strong>, which are shapes with four sides. To help students practice and understand this chapter better, extra questions have been created. These extra questions are like bonus exercises that give students more practice and help them explore quadrilaterals in more detail.<\/p>\n<p>The <strong>Class 8 Maths Chapter 3 Extra Questions<\/strong> cover various aspects of quadrilaterals, such as their properties, types, and how they are used. By solving these <strong>extra questions,<\/strong> students can improve their knowledge and skills in working with quadrilaterals. The questions also come with solutions, making it easier for students to check their answers and learn from their mistakes.<\/p>\n<p>These extra questions provide a fun and engaging way for students to learn more about quadrilaterals. They can practice identifying different types of quadrilaterals, understanding their features, and solving problems related to them. By working through these <strong>extra questions<\/strong>, students can boost their confidence in math and be better prepared for tests and exams.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_8_Maths_Chapter_3_Extra_Questions_with_Solutions_-_Understanding_Quadrilaterals\"><\/span>Class 8 Maths Chapter 3 Extra Questions with Solutions &#8211; Understanding Quadrilaterals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For Class 8 students learning about quadrilaterals, extra questions with solutions are a helpful tool. These extra questions from chapter 3 class 8 maths cover different aspects of quadrilaterals and come with answers to check your work. By practicing with these questions, students can improve their understanding of quadrilaterals and how to solve related problems.<\/p>\n<p>The solutions provided not only give the correct answers but also explain how to solve each question step by step. This resource helps students identify areas where they need more practice and enhances their overall grasp of quadrilaterals in a clear and straightforward manner.<\/p>\n<p>Get Extra Questions for Class 8 Maths on Infinity Learn for free.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/foundation-course-for-class-8?utm_source=surge&amp;utm_medium=interlinking\" target=\"_blank\" rel=\"noopener\"><button><strong>Enroll now to Online Class 8 Foundation Course<\/strong><\/button><\/a><\/p>\n<h3> Very Short Answer Type<\/h3>\n<p><strong>Question 1. In the given figure, ABCD is a parallelogram. Find x.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265738_0d572e59de_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q1\" width=\"190\" height=\"116\" \/><br \/>\n<strong>Solution: <\/strong> AB = DC [Opposite sides of a parallelogram]\n<p>3x + 5 = 5x \u2013 1<\/p>\n<p>\u21d2 3x \u2013 5x = -1 \u2013 5<\/p>\n<p>\u21d2 -2x = -6<\/p>\n<p>\u21d2 x = 3<\/p>\n<p><strong>Question 2. In the given figure find x + y + z.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265768_ac36d34c53_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q2\" width=\"160\" height=\"136\" \/><strong>Solution: <\/strong> We know that the sum of all a polygon&#8217;s outside angles equals 360\u00b0.<\/p>\n<p>x + y + z = 360\u00b0<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Question 3. In the given figure, find x.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964239927_785c1eee6c_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q3\" width=\"200\" height=\"141\" \/><strong>Solution: <\/strong> \u2220A + \u2220B + \u2220C = 180\u00b0 [Angle sum property]\n<p>(x + 10)\u00b0 + (3x + 5)\u00b0 + (2x + 15)\u00b0 = 180\u00b0<\/p>\n<p>\u21d2 x + 10 + 3x + 5 + 2x + 15 = 180<\/p>\n<p>\u21d2 6x + 30 = 180<\/p>\n<p>\u21d2 6x = 180 \u2013 30<\/p>\n<p>\u21d2 6x = 150<\/p>\n<p>\u21d2 x = 25<\/p>\n<p><strong>Question 4. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle.<\/strong><\/p>\n<p><strong>Solution: <\/strong> The sum of a quadrilateral&#8217;s internal angles equals 360\u00b0.<\/p>\n<p>Let the quadrilateral&#8217;s angles be 2x\u00b0, 3x\u00b0, 5x\u00b0, and 8x\u00b0.<\/p>\n<p>2x + 3x + 5x + 8x = 360\u00b0<\/p>\n<p>\u21d2 18x = 360\u00b0<\/p>\n<p>\u21d2 x = 20\u00b0<\/p>\n<p>Hence the angles are<\/p>\n<p>2 \u00d7 20 = 40\u00b0,<\/p>\n<p>3 \u00d7 20 = 60\u00b0,<\/p>\n<p>5 \u00d7 20 = 100\u00b0<\/p>\n<p>and 8 \u00d7 20 = 160\u00b0.<\/p>\n<p><strong>Question 5. Find the measure of an interior angle of a regular polygon of 9 sides.<\/strong><\/p>\n<p><strong>Solution: <\/strong> Measure of an interior angle of a regular polygon<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964292196_2c2a139cc1_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q5\" width=\"256\" height=\"187\" \/><\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-courses-cbse-class-8?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\"lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/01\/class-8-cbse-foundation-course.png\" alt=\"class 8 cbse foundation course\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/01\/class-8-cbse-foundation-course.png\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-courses-cbse-class-8?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<button><strong>Class 8 CBSE Foundation Course<\/strong><\/button><br \/>\n<\/a><\/p>\n<div style=\"text-align: left;\">The Class 8 CBSE Foundation Course is designed to be the most competitive educational program in India, providing an exceptional online learning experience. Our focused batch encompasses all crucial subjects, ensuring comprehensive preparation for students.<\/div>\n<\/div>\n<p><strong>Question 6. Length and breadth of a rectangular wire are 9 cm and 7 cm respectively. If the wire is bent into a square, find the length of its side.<\/strong><\/p>\n<p><strong>Solution: <\/strong> Perimeter of the rectangle = 2 [length + breadth]\n<p>= 2[9 + 7] = 2 \u00d7 16 = 32 cm.<br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265843_b2fa65a280_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q6\" width=\"210\" height=\"90\" \/><br \/>\nNow perimeter of the square = Perimeter of rectangle = 32 cm.<\/p>\n<p>Side of the square = \\(\\frac { 32 }{ 4 }\\) = 8 cm.<\/p>\n<p>Hence, the length of the side of square = 8 cm.<\/p>\n<p><strong>Question 7. I<\/strong><strong>n the given figure ABCD, find the value of x.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964292301_197bc414fb_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q7\" width=\"180\" height=\"124\" \/><br \/>\n<strong>Solution: <\/strong> 360\u00b0 is the sum of all a polygon&#8217;s outside angles.<br \/>\nx + 70\u00b0 + 80\u00b0 + 70\u00b0 = 360\u00b0<br \/>\n\u21d2 x + 220\u00b0 = 360\u00b0<br \/>\n\u21d2 x = 360\u00b0 \u2013 220\u00b0 = 140\u00b0<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Question 8. In the parallelogram given alongside if m\u2220Q = 110\u00b0, find all the other angles.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265733_1b516f8251_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q8\" width=\"163\" height=\"109\" \/><br \/>\n<strong>Solution: <\/strong> Given m\u2220Q = 110\u00b0<\/p>\n<p>Then m\u2220S = 110\u00b0 (Opposite angles are equal)<\/p>\n<p>Since \u2220P and \u2220Q are supplementary.<\/p>\n<p>Then m\u2220P + m\u2220Q = 180\u00b0<\/p>\n<p>\u21d2 m\u2220P + 110\u00b0 = 180\u00b0<\/p>\n<p>\u21d2 m\u2220P = 180\u00b0 \u2013 110\u00b0 = 70\u00b0<\/p>\n<p>\u21d2 m\u2220P = m\u2220R = 70\u00b0 (Opposite angles)<\/p>\n<p>Hence m\u2220P = 70, m\u2220R = 70\u00b0<\/p>\n<p>and m\u2220S = 110\u00b0<\/p>\n<p><strong>Question 9. In the given figure, ABCD is a rhombus. Find the values of x, y and z.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964291991_bcb1182590_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q9\" width=\"178\" height=\"115\" \/><br \/>\n<strong>Solution: <\/strong> AB = BC (Sides of a rhombus)<\/p>\n<p>x = 13 cm.<\/p>\n<p>Since the diagonals of a rhombus bisect each other<\/p>\n<p>z = 5 and y = 12<\/p>\n<p>Hence, x = 13 cm, y = 12 cm and z = 5 cm.<\/p>\n<p><strong>Question 10. In the given figure, ABCD is a parallelogram. Find x, y and z.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265678_f9c9cb7a88_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q10\" width=\"170\" height=\"128\" \/><strong>Solution: <\/strong> \u2220A + \u2220D = 180\u00b0 (Adjacent angles)<\/p>\n<p>\u21d2 125\u00b0 + \u2220D = 180\u00b0<\/p>\n<p>\u21d2 \u2220D = 180\u00b0 \u2013 125\u00b0<\/p>\n<p>x = 55\u00b0<\/p>\n<p>\u2220A = \u2220C [Opposite angles of a parallelogram]\n<p>\u21d2 125\u00b0 = y + 56\u00b0<\/p>\n<p>\u21d2 y = 125\u00b0 \u2013 56\u00b0<\/p>\n<p>\u21d2 y = 69\u00b0<\/p>\n<p>\u2220z + \u2220y = 180\u00b0 (Adjacent angles)<\/p>\n<p>\u21d2 \u2220z + 69\u00b0 = 180\u00b0<\/p>\n<p>\u21d2 \u2220z = 180\u00b0 \u2013 69\u00b0 = 111\u00b0<\/p>\n<p>Hence the angles x = 55\u00b0, y = 69\u00b0 and z = 111\u00b0<\/p>\n<p><strong>Question 11. Find x in the following figure. (NCERT Exemplar)<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964291946_351a21af71_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q11\" width=\"198\" height=\"202\" \/><strong>Solution: <\/strong> In the given figure \u22201 + 90\u00b0 = 180\u00b0 (linear pair)<\/p>\n<p>\u22201 = 90\u00b0<\/p>\n<p>Now, sum of exterior angles of a polygon is 360\u00b0, therefore,<\/p>\n<p>x + 60\u00b0 + 90\u00b0 + 90\u00b0 + 40\u00b0 = 360\u00b0<\/p>\n<p>\u21d2 x + 280\u00b0 = 360\u00b0<\/p>\n<p>\u21d2 x = 80\u00b0<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Short_Answer_Type\"><\/span>Short Answer Type<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 12. In the given parallelogram ABCD, find the value of x andy.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265633_57af903884_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q12\" width=\"188\" height=\"119\" \/><br \/>\n<strong>Solution: <\/strong> \u2220A + \u2220B = 180\u00b0<\/p>\n<p>3y + 2y \u2013 5 = 180\u00b0<\/p>\n<p>\u21d2 5y \u2013 5 = 180\u00b0<\/p>\n<p>\u21d2 5y = 180 + 5\u00b0<\/p>\n<p>\u21d2 5y = 185\u00b0<\/p>\n<p>\u21d2 y = 37\u00b0<\/p>\n<p>Now \u2220A = \u2220C [Opposite angles of a parallelogram]\n<p>3y = 3x + 3<\/p>\n<p>\u21d2 3 \u00d7 37 = 3x + 3<\/p>\n<p>\u21d2 111 = 3x + 3<\/p>\n<p>\u21d2 111 \u2013 3 = 3x<\/p>\n<p>\u21d2 108 = 3x<\/p>\n<p>\u21d2 x = 36\u00b0<\/p>\n<p>Hence, x = 36\u00b0 and y \u2013 37\u00b0.<\/p>\n<p><strong>Question 13. ABCD is a rhombus with \u2220ABC = 126\u00b0, find the measure of \u2220ACD.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964239767_6ab2c1800a_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q13\" width=\"188\" height=\"130\" \/><br \/>\n<strong>Solution: <\/strong><\/p>\n<p>\u2220ABC = \u2220ADC (Opposite angles of a rhombus)<\/p>\n<p>\u2220ADC = 126\u00b0<\/p>\n<p>\u2220ODC = \\(\\frac { 1 }{ 2 }\\) \u00d7 \u2220ADC (Diagonal of rhombus bisects the respective angles)<\/p>\n<p>\u21d2 \u2220ODC = \\(\\frac { 1 }{ 2 }\\) \u00d7 126\u00b0 = 63\u00b0<\/p>\n<p>\u21d2 \u2220DOC = 90\u00b0 (Diagonals of a rhombus bisect each other at 90\u00b0)<\/p>\n<p>In \u0394OCD,<\/p>\n<p>\u2220OCD + \u2220ODC + \u2220DOC = 180\u00b0 (Angle sum property)<\/p>\n<p>\u21d2 \u2220OCD + 63\u00b0 + 90\u00b0 = 180\u00b0<\/p>\n<p>\u21d2 \u2220OCD + 153\u00b0 = 180\u00b0<\/p>\n<p>\u21d2 \u2220OCD = 180\u00b0 \u2013 153\u00b0 = 27\u00b0<\/p>\n<p>Hence \u2220OCD or \u2220ACD = 27\u00b0<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Question 14. Find the values of x and y in the following parallelogram.<\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964239722_8f03fc9397_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q14\" width=\"210\" height=\"131\" \/><br \/>\n<strong>Solution: <\/strong> Since, the diagonals of a parallelogram bisect each other.<\/p>\n<p>OA = OC<\/p>\n<p>x + 8 = 16 \u2013 x<\/p>\n<p>\u21d2 x + x = 16 \u2013 8<\/p>\n<p>\u21d2 2x = 8<\/p>\n<p>x = 4<\/p>\n<p>Similarly, OB = OD<\/p>\n<p>5y + 4 = 2y + 13<\/p>\n<p>\u21d2 3y = 9<\/p>\n<p>\u21d2 y = 3<\/p>\n<p>Hence, x = 4 and y = 3<\/p>\n<div class=\"card\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-courses-hots-class-8?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/hots.png\" alt=\"class 8 hots course\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/hots.png\" \/><noscript><img style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/08\/hots.png\" alt=\"class 8 hots exam\" data-eio=\"l\" \/><\/noscript><\/a><\/p>\n<p style=\"text-align: center;\">The Class 8 HOTS Course enhances critical thinking and problem-solving skills through engaging activities and advanced learning techniques, ensuring academic excellence.<br \/>\n<a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-courses-hots-class-8?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>Class 8 HOTS Course<\/strong><\/button><\/a><\/p>\n<\/div>\n<p><strong>Question 15. Write true and false against each of the given statements.<\/strong><\/p>\n<p><strong>(a) Diagonals of a rhombus are equal.<\/strong><\/p>\n<p><strong>(b) Diagonals of rectangles are equal.<\/strong><\/p>\n<p><strong>(c) Kite is a parallelogram.<\/strong><\/p>\n<p><strong>(d) Sum of the interior angles of a triangle is 180\u00b0.<\/strong><\/p>\n<p><strong>(e) A trapezium is a parallelogram.<\/strong><\/p>\n<p><strong>(f) Sum of all the exterior angles of a polygon is 360\u00b0.<\/strong><\/p>\n<p><strong>(g) Diagonals of a rectangle are perpendicular to each other.<\/strong><\/p>\n<p><strong>(h) Triangle is possible with angles 60\u00b0, 80\u00b0 and 100\u00b0.<\/strong><\/p>\n<p><strong>(i) In a parallelogram, the opposite sides are equal.<\/strong><\/p>\n<p><strong>Solution: <\/strong><\/p>\n<p>(a) False<\/p>\n<p>(b) True<\/p>\n<p>(c) False<\/p>\n<p>(d) True<\/p>\n<p>(e) False<\/p>\n<p>(f) True<\/p>\n<p>(g) False<\/p>\n<p>(h) False<\/p>\n<p>(i) True<\/p>\n<p><strong>Question 16. The sides AB and CD of a quadrilateral ABCD are extended to points P and Q respectively. Is \u2220ADQ + \u2220CBP = \u2220A + \u2220C? Give reason.<\/strong><\/p>\n<p><strong>Solution: <\/strong><\/p>\n<p>Join AC, then<\/p>\n<p>\u2220CBP = \u2220BCA + \u2220BAC and \u2220ADQ = \u2220ACD + \u2220DAC (Exterior angles of triangles)<br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964291841_aa8f3e4935_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q16\" width=\"217\" height=\"131\" \/><br \/>\nTherefore,<\/p>\n<p>\u2220CBP + \u2220ADQ = \u2220BCA + \u2220BAC + \u2220ACD + \u2220DAC<\/p>\n<p>= (\u2220BCA + \u2220ACD) + (\u2220BAC + \u2220DAC)<\/p>\n<p>= \u2220C + \u2220A<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Higher_Order_Thinking_Skills_HOTS\"><\/span>Higher Order Thinking Skills (HOTS)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 17. The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.<\/strong><br \/>\n<strong><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265553_6fd334c98d_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q17\" width=\"164\" height=\"99\" \/><\/strong><br \/>\n<strong>Solution: <\/strong><\/p>\n<p>Let AD = x cm<\/p>\n<p>diagonal BD = 3x cm<\/p>\n<p>In right-angled triangle DAB,<\/p>\n<p>AD<sup>2<\/sup> + AB<sup>2<\/sup> = BD<sup>2<\/sup> (Using Pythagoras Theorem)<\/p>\n<p>x<sup>2<\/sup> + AB<sup>2<\/sup> = (3x)<sup>2<\/sup><\/p>\n<p>\u21d2 x<sup>2<\/sup> + AB<sup>2<\/sup> = 9x<sup>2<\/sup><\/p>\n<p>\u21d2 AB<sup>2<\/sup> = 9x<sup>2<\/sup> \u2013 x<sup>2<\/sup><\/p>\n<p>\u21d2 AB<sup>2<\/sup> = 8x<sup>2<\/sup><\/p>\n<p>\u21d2 AB = \u221a8x = 2\u221a2x<\/p>\n<p>Required ratio of AB : AD = 2\u221a2x : x = 2\u221a2 : 1<\/p>\n<p><strong>Question 18. If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is \u2206AMD = \u2206CNB? Give reason. (NCERT Exemplar)<\/strong><\/p>\n<p><strong>Solution: <\/strong><br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47964265548_c4b728aab3_o.png\" alt=\"Understanding Quadrilaterals NCERT Extra Questions for Class 8 Maths Q18\" width=\"229\" height=\"115\" \/>In triangles AMD and CNB,<\/p>\n<p>AD = BC (opposite sides of parallelogram)<\/p>\n<p>\u2220AMB = \u2220CNB = 90\u00b0<\/p>\n<p>\u2220ADM = \u2220NBC (AD || BC and BD is transversal.)<\/p>\n<p>So, \u2206AMD = \u2206CNB (AAS)<\/p>\n<p>&nbsp;<\/p>\n<p><img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-01.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-01\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-02.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-02\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-03.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-03\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-04.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-04\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-05.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-05\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-06.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-06\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-07.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-07\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-08.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-08\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-09.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-09\" \/><br \/>\n<img class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-10.png\" alt=\"understanding-quadrilaterals-ncert-extra-questions-for-class-8-maths-chapter-3-10\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In Class 8 Mathematics, Chapter 3 focuses on Understanding Quadrilaterals, which are shapes with four sides. To help students practice [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"extra questions class 8 maths chapter 3 questions and answers","_yoast_wpseo_title":"Class 8 Maths Chapter 3 Extra Questions Understanding Quadrilaterals","_yoast_wpseo_metadesc":"Get Extra Questions for Class 8 Maths on Infinity Learn for free. 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