\n(iii) \u2220E = 80\u00b0, \u2220F = 30\u00b0, EF = 5 cm<\/td>\n | (iii) \u2220P = 80\u00b0, PQ = 5 cm, \u2220R = 30\u00b0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Solution: \nIn \u0394DEF and \u0394PQR \n(i) \u2220D = 60\u00b0, \u2220F = 80\u00b0, DF = 5 cm \n\u2220Q = 60\u00b0, \u2220R = 80\u00b0, QR = 5 cm \n\u2220D = \u2220Q (Each 60\u00b0) \n\u2220F = \u2220R (Each 80\u00b0) \nIncluded side DF = QR \n\u0394DEF = \u0394QPR (ASA criterion) \n \n(ii) In \u0394DEF and \u0394PQR \n\u2220D = 60\u00b0, \u2220F = 80\u00b0, DF = 6 cm \n\u2220Q = 60\u00b0, \u2220R = 80\u00b0 and QP = 6 cm \nHere, \u2220D = \u2220Q (Each 80\u00b0) \n\u2220F = \u2220R (Each 80\u00b0) \nBut included side DF \u2260 QR \n\u0394DEF and \u0394PQR are not congruent. \n \n(iii) In \u0394DEF and \u0394PQR \n\u2220E = 80\u00b0, \u2220F = 30\u00b0, EF = 5 cm \n\u2220P = 80\u00b0, PQ = 5 cm, \u2220R = 30\u00b0 \nHere, \u2220E = \u2220P (Each = 80\u00b0) \n\u2220F = \u2220R (Each = 30\u00b0) \nBut inlcuded sides are not equal. \n\u0394DEF and \u0394PQR are not congruent. \n<\/p>\n Question 5. \nIn the adjoining figure, measures of some parts are indicated. \n(i) State three pairs of equal parts in triangles ABC and ABD. \n(ii) Is \u0394ABC = \u0394BAD? Give reasons. \n(iii) Is BC = AD? Why? \n \nSolution: \nIn the given figure, \n\u2220DAC = 45\u00b0, \u2220CAB = 30\u00b0, \u2220CBD = 45\u00b0 and \u2220DBA = 30\u00b0 \nNow in \u0394ABC and \u0394BAD, \n\u2220DAC + \u2220CAB = 45\u00b0 + 30\u00b0 = 75\u00b0 \nand \u2220CBD + \u2220DBA = 45\u00b0 + 30\u00b0 = 75\u00b0 \n\u2220DAB = \u2220CBA \nNow in \u0394ABC and \u0394DAB \nAB = AB (Common) \n\u2220CBA = \u2220DAB (Proved) \n\u2220CAB = \u2220DBA (Each = 30\u00b0) \n\u0394ABC = \u0394DAB (ASA criterion) \nYes, BC = AD (c.p.c.t.)<\/p>\n Question 6. \nIn the adjoining figure, ray AZ bisects \u2220DAB as well as \u2220DCB. \n(i) State the three pairs of equal parts in triangles BAC and DAC. \n(ii) Is \u0394BAC = \u0394DAC? Give reasons. \n(iii) Is CD = CB? Give reasons. \n \nSolution: \nIn the given figure \n\u2220DAC = \u2220BAC \n\u2220DCA = \u2220BCA \nNow in \u0394BAC and \u0394DAC \nAC = AC (Common) \n\u2220BAC = \u2220DAC (Given) \n\u2220BCA = \u2220DCA (Given) \n\u0394BAC = \u0394DAC (ASA criterion) \nYes,AB = AD (c.p.c.t.) \nYes, CD = CB (c.p.c.t.)<\/p>\n Question 7. \nExplain why \u0394ABC = \u0394FED? \n \nSolution: \nIn \u0394ABC and \u0394FED \nBC = DE \n\u2220B = \u2220E (Each = 90\u00b0) \n\u2220A = \u2220F \n\u2220C = 90\u00b0 – \u2220A and \u2220D = 90\u00b0 – \u2220F \nBut \u2220A = \u2220F (Given) \n\u2220C = \u2220D \nNow in \u0394ABC and \u0394DEF \nBC = DE (Given) \n\u2220B = \u2220E (Given 90\u00b0) \n\u2220C = \u2220D (Proved) \n\u0394ABC = \u0394DEF (ASA criterion)<\/p>\n Question 8. \nGiven below are the measurements of some parts of triangles. Examine whether the two triangles are congruent or not, using RHS congruence rule. In the case of congruent triangles, write the result in symbolic form:<\/p>\n \n\n\n\u0394ABC<\/strong><\/td>\n\u0394PQR<\/strong><\/td>\n<\/tr>\n\n(i) \u2220B = 90\u00b0, AC = 8 cm, AB = 3 cm<\/td>\n | (i) \u2220P = 90\u00b0, PR = 3 cm, QR = 8 cm<\/td>\n<\/tr>\n | \n(ii) \u2220A = 90\u00b0, AC = 5 cm, BC = 9 cm<\/td>\n | (ii) \u2220Q = 90\u00b0, PR = 8 cm, PQ = 5 cm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Solution: \nWe are given the measurement of some parts of the triangles. \nWe have to examine whether the two triangles are congruent \nor not using RHS congruency rule. \nIn \u0394ABC and \u0394PQR \n(i) \u2220B = 90\u00b0, AC = 8 cm, AB = 3 cm \n\u2220P = 90\u00b0, PR = 3 cm, QR = 8 cm \n \nWe see that in two \u0394s ABC and RPQ \n\u2220B = \u2220P (Each = 90\u00b0) \nSide AB = RP (Each = 3 cm) \nHypotenuse AC = RQ \n\u0394ABC = \u0394RPQ (RHS criterion) \n(ii) In \u0394ABC and \u0394PQR \n \n\u2220A = \u2220Q (Each = 90\u00b0) \nSide AC = QP (Each = 5 cm) \nBut hypotenuse BC and PR are not equal to each other. \nTriangles are not congruent.<\/p>\n Question 9. \nIn the given figure, measurements of some parts are given. \n(i) State the three pairs of equal parts in \u0394PQS and \u0394PRS. \n(ii) Is \u0394PQS = \u0394PRS? Give reasons. \n(iii) Is S mid-point of \\(\\bar { QR }\\) ? Why? \n \nSolution: \nIn the given figure, \nPQ = 3 cm, PR = 3 cm \nPS \u22a5 QR \n(i) Now in right \u0394PQS and \u0394PRS right angles at S. (\u2235 PS \u22a5 QR) \nside PS = PS (Common) \nHypotenuse PQ = PR (Each = 3 cm) \n(ii) \u0394PQS = \u0394PRS (RHS criterion) \n(iii) QS = SR (c.p.c.t.) \nS is the mid point of QR<\/p>\n Question 10. \nIn the given figure, O is mid-point of \\(\\bar { AB }\\) and \u2220A = \u2220B. Show that \u0394AOC = \u0394BOD. \n \nSolution: \nIn the given figure, \nO is the mid-point of AB \nAO = OB \nNow in \u0394AOC and \u0394BOD \nAO = OB (\u2235 O is mid-point of AB) \n\u2220A = \u2220B (Given) \n\u2220AOC = \u2220BOD (Vertically opposite angles) \n\u0394AOC = \u0394BOD (ASA criterion)<\/p>\n | | | |