{"id":6929,"date":"2021-03-12T10:17:58","date_gmt":"2021-03-12T04:47:58","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=6929"},"modified":"2021-09-15T11:38:58","modified_gmt":"2021-09-15T06:08:58","slug":"ap-board-8th-class-maths-solutions-chapter-8-ex-8-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-8th-class-maths-solutions-chapter-8-ex-8-1\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 8 Exploring Geometrical Figures Ex 8.1"},"content":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions<\/a> Chapter 8 Exploring Geometrical Figures Ex 8.1 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 8th Lesson Exploring Geometrical Figures Exercise 8.1<\/h2>\n

\"AP<\/p>\n

Question 1.
\nName five pairs of congruent objects, you use daily.
\nSolution:
\nSolution:
\ni) Pair of ear rings.
\nii) Wheels of a cycle.
\niii) Equal lengths of scales.
\niv) Pair of bangles.
\nv) Mathematics textbooks of same class.<\/p>\n

Question 2.
\n(a) Draw two congruent figures. Are they similar? Explain
\n(b) Take two similar shapes. If you slide rotate or flip one of them, does the similarity remain?
\nSolution:
\na) \u0394ABC \u2245 \u0394PQR
\n\"AP
\nFrom \u0394ABC & \u0394PQR
\nAB = PQ
\nAC = PR
\nBC = QR
\n\u2220A = \u2220P
\n\u2220B = \u2220Q
\n\u2220C = \u2220R
\n\u2234 Congruent triangles are similar to each other.
\nBut similar triangles are not congruent.<\/p>\n

\"AP<\/p>\n

b)
\n\"AP
\nFrom fig. \u0394XYZ and \u0394STU are similar triangles. If these triangles are rotated even they are similar to each other.<\/p>\n

Question 3.
\nIf \u0394 ABC \u2245 \u0394 NMO, name the congruent sides and angles.
\nSolution:
\n\"AP
\nFrom the congruent triangles
\n\u0394ABC \u2245 \u0394NMO
\nAB = NM
\nBC = MO
\nAC = NO
\n\u2220A = \u2220N
\n\u2220B =\u2220M
\n\u2220C = \u2220O<\/p>\n

Question 4.
\nState whether the following statements are true. Explain with reason.
\n(i) Two squares of side 3 cm each and one of them rotated through 45\u00b0 are congruent.
\n(ii) Any two right triangles with hypotenuse 5 cm, are congruent.
\n(iii) Any two circles of radii 4 cm each are congruent.
\n(iv) Two equilateral triangles of side 4 cm each but labeled as A ABC and A LHN arc not congruent.
\n(v) Mirror image of a polygon is congruent to the original.
\nSolution:
\ni) True. If the square is rotated 45\u00b0 then it is remaining congruent.
\nii) True. If the hypotenuse of two right triangles are equal, then the two triangles are congruent to each other, [\u2235 Their corresponding sides and angles will also be equal]
\n\"AP
\n(iii) True
\nSince they are having equal radii (r1<\/sub> = r2<\/sub> = 4 cm )
\n= 4 cm).
\n\u2234 The given circles are congruent.<\/p>\n

\"AP<\/p>\n

iv) False.
\nIf two sides of one triangle are equal to the corresponding two sides of another triangle, then the third sides are in the proportion.
\n\u2234 \u0394ABC \u2245 \u0394LHN
\n\"AP
\nBut given tXABC,\u2019L\\LHN. Then it is false.<\/p>\n

v) True.
\nAlways the mirror images of a polygon is congruent to the original.<\/p>\n

Question 5.
\nDraw a polygon on a square dot sheet. Also draw congruent figures in different directions and mirror image of it.
\nSolution:
\n\"AP<\/p>\n

Question 6.
\nUsing a square dot sheet or a graph sheet draw a rectangle and construct a similar figure.
\nFind the perimeter and areas of both and compare their ratios with the ratio of their
\ncorresponding sides.
\nSolution:
\n\"AP
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 7.
\n7 pillars are used to hold a slant iron gudder as shown in the figure. If the distance between every two pillars is 1 m and height of the last piller is 10.5 m. Find the height of pillar.
\n\"AP
\nSolution:
\n\"AP
\nThe height of the 1st pillar
\nh1<\/sub> = \\(\\frac{1}{7}\\) x 10.5 = 1.5m.<\/p>\n

The height of 2nd pillar
\nh2<\/sub> = \\(\\frac{2}{7}\\) x 10.5 = 3m.<\/p>\n

The height of 3rd pillar
\nh3<\/sub> = \\(\\frac{3}{7}\\) x 10.5 = 4.5 m.<\/p>\n

The height of 4th pillar
\nh4<\/sub> = \\(\\frac{4}{7}\\) x 10.5 = 6 m.<\/p>\n

The height of 5th pillar
\nh5<\/sub> = \\(\\frac{5}{7}\\) x 10.5 = 7.5 m.<\/p>\n

The height of 6th pillar
\nh6<\/sub> =\\(\\frac{6}{7}\\) x 10.5 = 9 m.<\/p>\n

\"AP<\/p>\n

Question 8.
\nStanding at 5 m apart from a vertical pole of height 3 m, Sudha observed a building at the back of the piller that tip of the pillar is in line with the top of the building. If the distance
\nbetween pillar and building is 10 m, estimate the height of the building. [Here height of
\nSudha is neglected]
\nSolution:
\n\u0394AOAB ~ \u0394OCD
\nThe corresponding sides of similar triangles are in a same proportion^?
\n\"AP
\n\u21d2 h = 3 x 3 = 9
\n\u2234 h = height of a building = 9 mts.<\/p>\n

Question 9.
\nDraw a quadrilateral of any measurements. Construct a dilation of scale factor 3. Measure their corresponding sides and verify whether they are similar.
\nSolution:
\n\"AP
\nObserve the following dilation ABCD, it is a square drawn on a graph sheet.
\nAll vertices A, B, C, D are joined from the sign \u2019O\u2019 and produced to 3 times the length upto A’, B\u2019, C\u2019 and D\u2019 respec\u00actively. Then A\u2019, B’, C’, D’ are joined to form a rectangle which 3 times has enlarged sides of ABCD. Here, 0 is called centre of dilation and \\(\\frac{\\mathrm{OA}^{\\prime}}{\\mathrm{OA}}=\\frac{3}{1}\\) = 3 is called scale factor.
\n\u2234 \u25a1 ABCD ~ \u25a1 A’B’C’D’
\n[ \u2235 their corresponding sides are equal]
\n\"AP<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 8 Exploring Geometrical Figures Ex 8.1 Textbook Questions and Answers. AP State Syllabus 8th Class Maths Solutions 8th Lesson Exploring Geometrical Figures Exercise 8.1 Question 1. Name five pairs of congruent objects, you use daily. Solution: Solution: i) Pair of ear rings. ii) Wheels of …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/6929"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=6929"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/6929\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=6929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=6929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=6929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}