{"id":42952,"date":"2023-04-04T14:31:52","date_gmt":"2023-04-04T09:01:52","guid":{"rendered":"https:\/\/icsesolutions.com\/?p=42952"},"modified":"2023-04-05T10:09:18","modified_gmt":"2023-04-05T04:39:18","slug":"ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-objective-type-questions","status":"publish","type":"post","link":"https:\/\/icsesolutions.com\/ml-aggarwal-class-7-solutions-for-icse-maths-chapter-12-objective-type-questions\/","title":{"rendered":"ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions"},"content":{"rendered":"

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions<\/h2>\n

Mental Maths<\/strong><\/p>\n

Question 1.
\nFill in the blanks:
\n(i) Two line segments are congruent if ……….
\n(ii) Among two congruent angles, one has a measure of 63\u00b0; the measure of the other angle is ……….
\n(iii) When we write \u2220A = \u2220B, we actually mean ………
\n(iv) The side included between \u2220M and \u2220N of \u2206MNP is ……….
\n(v) The side QR of \u2206PQR is included between angles ……….
\n(vi) If two triangles ABC and PQR are congruent under the correspondence A \u2194 R, B \u2194 P and C \u2194 Q, then in symbolic form it can be written as \u2206ABC = ………
\n(vii) If \u2206DEF = \u2206SRT, then the correspondence between vertices is ……….
\nSolution:
\n(i) Two line segments are congruent if they are of the same length.
\n(ii) Among two congruent angles, one has a measure of 63\u00b0;
\nthe measure of the other angle is 63\u00b0.
\n(iii) When we write \u2220A = \u2220B, we actually mean m\u2220A = m\u2220B.
\n(iv) The side included between \u2220M and \u2220N of \u2206MNP is MN.
\n(v) The side QR of \u2206PQR is included between angles \u2220Q and \u2220R.
\n(vi) If two triangles ABC and PQR are congruent
\nunder the correspondence A \u2194 R, B \u2194 P and C \u2194 Q,
\nthen in symbolic form it can be written as \u2206ABC = \u2206RPQ.
\n(vii) If \u2206DEF = \u2206SRT, then the correspondence between vertices is
\nD \u2194 S, E \u2194 R and F \u2194 T.<\/p>\n

Question 2.
\nState whether the following statements are true (T) or false (F):
\n(i) All circles are congruent.
\n(ii) Circles having equal radii are congruent.
\n(iii) Two congruent triangles have equal areas and equal perimeters.
\n(iv) Two triangles having equal areas are congruent.
\n(v) Two squares having equal areas are congruent.
\n(vi) Two rectangles having equal areas are congruent.
\n(vii) All acute angles are congruent.
\n(vii)All right angles are congruent.
\n(ix) Two figures are congruent if they have the same shape.
\n(x) A two rupee coin is congruent to a five rupee coin.
\n(xi) All equilateral triangles are congruent.
\n(xii) Two equilateral triangles having equal perimeters are congruent.
\n(xii) If two legs of one right triangle are equal to two legs of another right angle triangle, then the two triangles are congruent by SAS rule.
\n(xiv) If three angles of two triangles are equal, then triangles are congruent.
\n(xv) If two sides and one angle of one triangle are equal to two sides and one angle of another triangle, then the triangle are congruent.
\nSolution:
\n(i) All circles are congruent. (False)
\nCorrect:
\nAs if all circles have equal radii otherwise not.
\n(ii) Circles having equal radii are congruent. (True)
\n(iii) Two congruent triangles have equal areas
\nand equal perimeters. (True)
\n(iv) Two triangles having equal areas are congruent. (False)
\nCorrect:
\nAs they may have different sides and angles.
\n(v) Two squares having equal areas are congruent. (True)
\n(vi) Two rectangles having equal areas are congruent. (False)
\nCorrect:
\nAs their side can be different.
\n(vii) All acute angles are congruent. (False)
\nCorrect:
\nAs acute angles have different measures.
\n(viii) All right angles are congruent. (True)
\n(ix) Two figures are congruent if they have the same shape. (False)
\nCorrect:
\nAs the same shapes have different measures.
\n(x) A two rupee coin is congruent to a five rupee coin. (False)
\nCorrect:
\nAs they have different size.
\n(xi) All equilateral triangles are congruent. (False)
\nCorrect:
\nAs they have different sides in length.
\n(xii) Two equilateral triangles having equal perimeters are congruent. (True)
\n(xiii) If two legs of one right triangle are equal to
\ntwo legs of another right angle triangle,
\nthen the two triangles are congruent by SAS rule. (True)
\n(xiv) If three angles of two triangles are equal,
\nthen triangles are congruent. (False)
\nCorrect:
\nThey can be similar to each other.
\n(xv) If two sides and one angle of one triangle are equal to two sides
\nand one angle of another triangle, then the triangle is congruent. (False)
\nCorrect:
\nIf the angles are included, they can be congruent.<\/p>\n

Multiple Choice Questions<\/strong><\/p>\n

Choose the correct answer from the given four options (3 to 14):
\nQuestion 3.
\nWhich one of the following is not a standard criterion of congruency of two triangles?
\n(a) SSS
\n(b) SSA
\n(c) SAS
\n(d) ASA
\nSolution:
\nThe axiom SSA is not a standard criterion
\nof congruency of triangles. (b)<\/p>\n

Question 4.
\nIf \u2206ABC = \u2206PQR and \u2220CAB = 65\u00b0, then \u2220RPQ is
\n(a) 65\u00b0
\n(b) 75\u00b0
\n(c) 90\u00b0
\n(d) 115\u00b0
\nSolution:
\n\u2206ABC = \u2206PQR
\n\"ML
\n\u2220CAB = 65\u00b0
\n\u2220RPQ = 65\u00b0 (corresponding angles) (a)<\/p>\n

Question 5.
\nIf \u2206ABC = \u2206EFD, then the correct statement is
\n(a) \u2220A = \u2220D
\n(b) \u2220A = \u2220F
\n(c) \u2220A = \u2220E
\n(d) \u2220B = \u2220E
\nSolution:
\n\u2206ABC = \u2206EFD
\nThen \u2220A = \u2220E (c)
\n\"ML<\/p>\n

Question 6.
\nIf \u2206ABC = \u2206PQR, then the correct statement is
\n(a) AB = QR
\n(b) AB = PR
\n(c) BC = PR
\n(d) AC = PR
\nSolution:
\n\u2206ABC = \u2206PQR
\n\"ML
\nThen AB = PQ
\nAC = PR (d)<\/p>\n

Question 7.
\nIf \u2220D = \u2220P, \u2220E = \u2220Q and DE = PQ, then \u2206DEF = \u2206PQR, by the congruence rule
\n(a) SAS
\n(b) ASA
\n(c) SSS
\n(d) RHS
\nSolution:
\nIn \u2206DEF = \u2206PQR
\n\u2220D = \u2220P, \u2220E = \u2220Q
\nDE = PQ
\n\u2206DEF = \u2206PQR (ASA axiom) (b)<\/p>\n

Question 8.
\nIn \u2206ABC and \u2206PQR, BC = QR and \u2220C = \u2220R. To establish \u2206ABC = \u2206PQR by SAS congruence rule, the additional information required is
\n(a) AC = PR
\n(b) AB = PR
\n(c) CA = PQ
\n(d) AB = PQ
\nSolution:
\nIf \u2206ABC = \u2206PQR by SAS
\nBC = QR and \u2220C = \u2220R, then AC = PR (a)<\/p>\n

Question 9.
\nIn the given figure, the lengths of the sides of two triangles are given. The correct statement is
\n(a) \u2206ABC = \u2206PQR
\n(b) \u2206ABC = \u2206QRP
\n(c) \u2206ABC = \u2206QPR
\n(d) \u2206ABC = \u2206RPQ
\n\"ML
\nSolution:
\nCorrect statement is \u2206ABC = \u2206QRP. (b)<\/p>\n

Question 10.
\nIn the given figure, M is the mid-point of both AC and BD. Then
\n(a) \u22201 = \u22202
\n(b) \u22201 = \u22204
\n(c) \u22202 = \u22204
\n(d) \u22201 = \u22203
\n\"ML
\nSolution:
\nIn the given figure,
\nM is mid-point of AC and BD both then \u22201 = \u22204. (b)<\/p>\n

Question 11.
\nIn the given figure, \u2206PQR = \u2206STU. What is the length of TU?
\n(a) 5 cm
\n(b) 6 cm
\n(c) 7 cm
\n(d) cannot be determined
\n\"ML
\nSolution:
\nIn the given figure,
\n\u2206PQR = \u2206STU
\nTU = QR = 6 cm (b)<\/p>\n

Question 12.
\nIn the given figure, \u2206ABC and \u2206DBC are on the same base BC. If AB = DC and AC = DB, then which of the following statement is correct?
\n(a) \u2206ABC = \u2206DBC
\n(b) \u2206ABC = \u2206CBD
\n(c) \u2206ABC = \u2206DCB
\n(d) \u2206ABC = \u2206BCD
\n\"ML
\nSolution:
\nIn the given figure,
\nAB = DC, AC = DB
\nThen, \u2206ABC = \u2206DCB (c)<\/p>\n

Question 13.
\nThe two triangles shown in the given figure are:
\n(a) congruent by AAS rule
\n(b) congruent by ASA rule
\n(c) congruent by SAS rule
\n(d) not congruent.
\n\"ML
\nSolution:
\nIn the given two triangles are not congruent.
\nIn first triangle, AAS are given while in second ASA are given. (d)<\/p>\n

Question 14.
\nIn .the given figure, \u2206ABC = \u2206PQR. The values of x and y are:
\n(a) x = 63, y = 35
\n(b) x = 77, y = 35
\n(c) x = 35, y = 77
\n(d) x = 63, y = 40
\n\"ML
\nSolution:
\nIn the given figure,
\n\u2206ABC = \u2206PQR
\n\u2220A = \u2220P and \u2220B = \u2220Q
\nNow x – 7 = 70\u00b0
\n\u21d2 x = 70\u00b0 + 7 = 77\u00b0
\nand 2y + 5 = 75
\n\u21d2 2y = 75\u00b0 – 5 = 70\u00b0
\n\u21d2 y = 35\u00b0
\nx = 77\u00b0, y = 35\u00b0 (b)<\/p>\n

Higher Order Thinking Skills (HOTS)<\/strong><\/p>\n

Question 1.
\nIf all the three altitudes of a triangle are equal, then prove that it is an equilateral triangle.
\nSolution:
\nGiven: In \u2206ABC,
\nAD, BE and CF are altitudes of the triangle
\nand AD = BE = CF.
\n\"ML
\nTo prove: \u2206ABC is an equilateral.
\nProof: In \u2206ABD and \u2206CFB
\nAD = CF (Given)
\n\u2220D = \u2220F (Each = 90\u00b0)
\n\u2220B = \u2220B (Common)
\n\u2206ABD = \u2206CFB (AAS criterion)
\nAB = BC …….(i)
\nSimilarly in \u2206BEC and \u2206ADC
\nBE = AD (Given)
\n\u2220C = \u2220C (Common)
\n\u2220E = \u2220D (Each = 90\u00b0)
\n\u2206BEC = \u2206ADC (AAS criterion)
\nBC = AC ………(ii)
\nFrom (i) and (ii)
\nAB = BC = AC
\n\u2206ABC is an equilateral triangle.<\/p>\n

Question 2.
\nIn the given fig., if BA || RP, QP || BC and AQ = CR, then prove that \u2206ABC = \u2206RPQ.
\n\"ML
\nSolution:
\nIn the given figure, BA || RP
\nQP || BC and AQ = CR
\nTo prove : \u2206ABC = \u2206RPQ
\nProof: AQ = CR
\nAdding CQ to both sides
\nAQ + CQ = CR + CQ
\n\u21d2 AC = RQ
\nNow in \u2206ABC and \u2206RPQ
\n\u2220A = \u2220R (Alternate angles)
\n\u2220C = \u2220Q (Alternate angles)
\nAC = RQ (Proved)
\n\u2206ABC = \u2206RPQ (ASA criterion)
\n\"ML<\/p>\n

ML Aggarwal Class 7 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Objective Type Questions Mental Maths Question 1. Fill in the blanks: (i) Two line segments are congruent if ………. (ii) Among two congruent angles, one has a measure of 63\u00b0; the measure of the other angle is ………. (iii) When we write …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3034],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42952"}],"collection":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/comments?post=42952"}],"version-history":[{"count":1,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42952\/revisions"}],"predecessor-version":[{"id":159000,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/42952\/revisions\/159000"}],"wp:attachment":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/media?parent=42952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/categories?post=42952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/tags?post=42952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}