{"id":5656,"date":"2021-03-05T15:01:31","date_gmt":"2021-03-05T09:31:31","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=5656"},"modified":"2021-09-15T11:39:28","modified_gmt":"2021-09-15T06:09:28","slug":"ap-board-9th-class-maths-solutions-chapter-7-intext-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-9th-class-maths-solutions-chapter-7-intext-questions\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 7 Triangles InText Questions"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 7 Triangles InText Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 7th Lesson Triangles InText Questions<\/h2>\n

\"AP<\/p>\n

Do This<\/strong><\/p>\n

Question 1.
\nThere are some statements given below. Write whether they are true or false. [Page No. 150]
\nSolution:
\ni) Two circles are always congruent. – False
\nii) Two line segments of same length are always congruent. – True
\niii) Two right angle triangles are some times congruent. – True
\niv) Two equilateral triangles with their sides equal are always congruent. – True<\/p>\n

Question 2.
\nWhich minimum measurements do you require to check if the given figures are congruent? [Page No. 150]<\/p>\n

i) Two rectangles.
\nSolution:
\nLength and breadth are required.<\/p>\n

ii) Two rhombuses.
\nSolution:
\nOne side and one interior angle are required.<\/p>\n

\"AP<\/p>\n

Do These<\/strong><\/p>\n

Question 1.
\nState whether the following triangles are congruent or not. Give reasons for your answer. [Page No. 153]
\n\"AP
\nSolution:
\ni) \u0394ABC \u2245 \u0394DEF
\n\u2235 \u2220B = \u2220E (\u2235 Angle sum property Z E = 180\u00b0 – (70\u00b0 + 60\u00b0) = 50\u00b0)
\nBC = EF
\n\u2220C = \u2220F
\n\u2234 By SAS congruence
\n\u0394ABC \u2245 \u0394DEF<\/p>\n

ii) In \u0394MNL and \u0394TSR
\nMN = ST
\nNL = TR
\n\u2220 M = \u2220 T (\u2235 \u0394MNL is flipped to get \u0394TSR)
\n\u2234 \u0394MNL \u2245 \u0394TSR<\/p>\n

\"AP<\/p>\n

Question 2.
\nIn the given figure, the point P bisects AB and DC. Prove that \u0394APC \u2245 \u0394BPD. [Page No. 153]
\n\"AP
\nSolution:
\nGiven that P bisects AB and DC.
\nNow in \u0394APC and \u0394BPD
\nAP = BP (\u2235 P bisects AB)
\nCP = DP (\u2235 P bisects CD)
\n\u2220 APC = \u2220 BPD
\n\u2234 \u0394APC \u2245 \u0394RPP (\u2235 SAS congruence)<\/p>\n

Activity
\n<\/strong><\/p>\n

\"AP
\n1. On a tracing paper draw a line segment BC of length 6 cm.
\n2. From vertices B and C draw rays with angle 600 each. Name the point A where they meet
\n3. Fold the paper so that B and C fit precisely on top of each other. What do you observe? Is AB = AC?
\n[Page No. 160]<\/p>\n

\"AP<\/p>\n

Do This<\/strong><\/p>\n

Question 1.
\nIn the figure given below \u0394ABC and \u0394DBC are two triangles such that \\(\\overline{\\mathbf{A B}}=\\overline{\\mathbf{B D}}\\) and \\(\\overline{\\mathbf{A C}}=\\overline{\\mathbf{C D}}\\) . Show that \u0394ABC \u2245 \u0394DBC [Page No. 164]
\n\"AP
\nSolution:
\nGiven that \\(\\overline{\\mathbf{A B}}=\\overline{\\mathbf{B D}}\\) and \\(\\overline{\\mathbf{A B}}=\\overline{\\mathbf{B D}}\\)<\/p>\n

In \u0394ABC and \u0394DBC
\nAB = BD (\u2235 given)
\nAC = DC (\u2235 given)
\nBC = BC (common side)
\n\u2234 \u0394ABC \u2245 \u0394DBC
\n( \u2235 by SSS congruence)<\/p>\n

\"AP<\/p>\n

Activity<\/strong><\/p>\n

Question 1.
\nConstruct a right angled triangle with hypotenuse 5 cm. and one side 3 cm. long. How many different triangles can be constructed? Compare your triangle with those of the other members of your class. Are the triangles congruent? Cut them out and place one triangle over the other with equal side placed on each other. Turn the triangle if necessary what do you observe? You will find that two right triangles are congruent, if side and hypotenuse of one triangle are respectively equal to the corresponding side and hypotenous of other triangle.
\n[Page No. 165]<\/p>\n

Activity<\/strong><\/p>\n

Question 1.
\nDraw a triangle ABC mark a point A’ on CA produced (new position of it)
\nSo A\u2019C > AC (Comparing the lengths) Join A to B and complete the triangle ABC.<\/p>\n

What can you say about \u2220A\u2019BC and \u2220ABC ?
\nCompare them. What do you observe?
\n\"AP<\/p>\n

Clearly, \u2220A\u2019BC > \u2220ABC Continue to mark more points on CA (extended) and draw the triangles with the side BC and the points marked. You will observe that as the length of the side AC is increases (by taking different positions of A), the angle opposite to it, that is \u2220B also increases.
\n[Page No. 169]<\/p>\n

\"AP<\/p>\n

Question 2.
\nConstruct a scalene triangle ABC (that is a triangle in which all sides are of different lengths). Measure the lengths of the sides.
\n\"AP
\nNow, measure the angles. What do you observe?
\nIn \u0394ABC figure, BC is the longest side and AC is the shortest side. \u2018
\nAlso, \u2220A is the largest and \u2220B is the smallest.
\nMeasure angles and sides of each of the above triangles, what is the rela tion between a side and its opposite angle when compared with another pair?
\n\"AP<\/p>\n

Activity<\/strong><\/p>\n

Question
\nDraw a line segment AB. With A as centre and some radius, draw an arc and mark different points say P, Q, R, S, T on it.
\nSolution:
\n\"AP
\nJoin each of these points with A as well as with B (see figure). Observe that as we move from P to T, \u2220A is becoming larger and larger. What is happening to the length of the side opposite to it? Observe that the length of the side is also increasing; that is \u2220TAB > \u2220SAB > \u2220RAB > \u2220QAB > \u2220PAB
\nand TB > SB > RB > QB > PB.
\nNow, draw any triangle with all angles unequal to each other. Measure the lengths of the sides (see figure).
\n\"AP<\/p>\n

Observe that the side opposite to the largest angle is the longest. In figure, ZB is the largest angle and AC is the longest side
\nRepeat this activity for some more triangles and we see that the converse of the above Theorem is also true.<\/p>\n

Measure angles and sides of each triangle given below. What relation you can visualize for a side and its opposite angle in each triangle.
\n\"AP
\nIn this way, we arrive at the following theorem. [Page No. 170]<\/p>\n

\"AP<\/p>\n

Do This<\/strong><\/p>\n

Question
\nDraw a triangle ABC and measure its sides. Find the sum of the sides AB + BC, BC + AC; and AC + AB, compare it with the length of the third side. What do you observe ?
\n[Page No. 171]
\nSolution:
\n\"AP
\nAB + BC = 4 + 3 = 7
\n= 7 > 4 = AC
\nBC + CA > AB;
\n3 + 4 > 4
\nCA + AB > BC;
\n4 + 4 > 3<\/p>\n

DE + EF > DF
\nEF + DF > DE
\nFD + DE > EF
\n\u2234 Sum of any two sides of a triangle is greater than the third side.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 7 Triangles InText Questions and Answers. AP State Syllabus 9th Class Maths Solutions 7th Lesson Triangles InText Questions Do This Question 1. There are some statements given below. Write whether they are true or false. [Page No. 150] Solution: i) Two circles are always congruent. – …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5656"}],"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=5656"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5656\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=5656"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=5656"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=5656"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}