Page 3 :
Given Four Sides and an Angle, , 0 J: Construct a quadrilateral BOAT in which, = 4m, OA = 3.6m, AT = 4.2 cm, BT = 4.8m,, and 20 = 79°,, Solution; r, Step 1: Draw a rough, sketch of quadrilateral, BOAT, given BO = 4m,, OA = 3.6m, AT = 4.2 cm,, BT = 4.8 cm, and ZO=70°., Step 2: Draw a line, segment BO of length 4 cm., Step 3: Construct an angle of 70° at O., Step 4: With O as centre and radius 3.6 cm draw an, arc intersecting OX at point A., Step 5: With A as centre and radius 4.2 cm draw an, , arc., Step 6: Draw another, arc with B as the centre, and radius 4.8 cm, intersecting the arc, drawn previously at T., Step 7: Join BT and AT., Hence, BOAT is the, required quadrilateral,, , forgone te,, 1. Construct a quadrilateral ABCD in which, , AB = BC = 35m, AD = CD = $m, and, <ARC = 120°., , | 2. Construct a quadrilateral ABCD in which, AB = 3m, BC = 34m, CD «27 em,, DA =3.$ cm, and ZA = 70",, , , , Given Three Sides and Two Diagonals, , Example 4: Construct a quadrilateral MNOP in which, MN = 4m, NO = 3.8 cm, MP = 3 cm, diagonal, , MO = S cm, and diagonal NP = 4.6m., , Solution:, , Step 1: Draw a rough Pp o, sketch of quadrilateral eh |, MNOP, given MN = 4m }, , 3 o*, Mam, NO = 3.8m, MP = 3m, - Rog y, , diagonal MO = $ cm, and &, diagonal NP = 4.6m., Step 2: Draw a line, segment MN of length 4cm., Step 3: With M as centre and radius 5 cm draw an are, above the line segment MN., , , , M ton Nx, Rough sketch, , , , , , intersecting, Step 5: Draw \, <ENT = 110° at N., , re and FAIS 9.5 CN Ary, previous are at, , it . ting the, - inter, , alt to D, centre and radius Jem, day, a, , and radius 4.6 6m, dra,, , s centre lously drawn «, : ¢ previously Criwn ar. ., mersectinE the p' out, , and MP., nani MNOP, is the a 1 / P Me, quadri : jem “a,, [Note: | “@ ~, , . is are ij 4, , jagonal, — as doned, , lines], , Lijit, , adrilateral ABCD in which, : ae a RC = 3.2m. AD = 2.9m,, = 36cm,, canal 4C 2 4.Sem, and diagonal, 42cm, 2. pate quadniateral LMNO tn which, . LN «LO «65cm. MN = Tem, MO = 9 em,, and NO = Scm Also, find the length of the, , remaining side, , Mon, , , , , , , , , , , Given Three Sides and Two Included, Angles, , Example $: Constract a quadrilateral NEST in which, NEw 3.8m, £NES #78", ES @ 4.2 om,, , LENT @ WO", and NT ® 44 om, , Solution: r, , Step |: Draw a rough, shetch of the quadrilateral, NEST, given NE = 3.8 om., <NES © 73", ES @ 42cm,, <ENT © 110", and, , AT eticm N, Step 2: Draw a line, , seement NE of length 3., , Step 3: Constract - xe, <NES 37S at & Tr ‘, Step 4: With £ as i =, , 44am ile, , Centre and radius, t2em draw an are, , Xas 44cm

Page 4 :
ye, , _with Nas centre and radius 4.4 ¢, # vcting NY at T and join Ts., se qadeltral NEST thus obtained, is the, , Fo quadrilateral., , m, draw an, , , , , , , , , struct a quadrilateral MORE in which, , 1 2 3.5m. OR = 4.8 em, RE= 4.5 cm,, 10? 125°, and ZR = 60°,, , 10 sastruct a quadrilateral SENT in which, g£=70m. EN=5.8 em, NT = 2.5 cm,, , gse45*. and ZE = 90°., , avon two adjacent sides and three, angles, , people 6; Construct a quadrilateral SALE in which, getsom ZSAL = 100°, AL=4 cm,, , ME= 90". and ZASE = 60°., , Daw a rough sketch, , qte quodrilateral SALE, L, paSi=45cm,, , Sil= 100°, AL=4 cm,, , MWE= 90°, and ZASE = 60°. a, {ep 2: Draw a line segment S Asem {0A, Gofkength 4.5 cm., , {ep 3: Construct an angle of, WF aA., , Sep 4: With A as centre, ni radius 4 cm, draw, ‘peccutting AX at L., Sep §: Construct an, tale of 90° at L., , Sep 6; Construct the, tre ZASZ = 60° at, SName the point of, Tenection of LY and, Qasé, , lence, SALE is the required quadrilateral., , Rough sketch, , s 45em A, , Fantini, , '. Construct a quadrilateral PLAY in which, | PL=6cm,LA=4.5 cm, 2P= 60",, <L = 105°, and 2A = 80°., , 2 Isit possible to construct a quadrilateral, ABCD in which BC = 6 cm, CD =5.5 cm,, 2B = 95°, ZC = 120°, and ZD = 150°? Give, Teasons,, , , , , , , , CONSTRUCTION OF A SQUARE, We have studied that to construct a unique, quadrilateral, a minimum of five specific clements, are required to be known. However, WE will now, see that by using their properties, it is possible, to construct certain quadrilaterals given less than, five element measures. ;, Square is a quadrilateral in which all the sides are, of equal length and each angle is a right angle., Let us recall the basic properties of a square., * All the sides of a square are 4g, equal. Pi, + All the angles of a square = % =, are equal to 90°. /, * Thediagonals are equaland py, BC, perpendicular bisectors of, one another., Using the properties of a square, let us try to, construct it given some specific parameters., When One Side is Given, Example 7; Construct a square of side 5 cm., Solution;, Step 1: Let us draw a rough A__Sem_D, sketch of the square ABCD, with the side length 5 cm. Sem Sem, We have, AB = BC = CD =, DA= 5 cm and angles ZA =, ZB=2C=2ZD=90°. B Sem C, Step 2: Draw a line segment Rough sketch =, AB of length 5 cm. EI, Step 3: With the help of compass, construct a », perpendicular at point A by taking A as the centre and x, a convenient radius less than half of AB. 3, Step 4: Similarly, with the help of compass, construct 4, a perpendicular at point B. =, Step 5: With A and B as centres and radius 5 cm, draw 3, ares which intersect the perpendiculars at D and C é, respectively. 5, Step 6: Join C and D., Hence, ABCD is the, required square with, side 5 cm. 3, (Note: Use a ruler, and check whether sca, CD is Scm or not., Ifit is 5 cm, the, construction is, correct)

Page 5 :
a, , When One Diagonal is Given, , irene $: Construct a square ABCD, cach of whos?, “agonals measure 8 cm,, , Solution: We know that, the p, diagonals of a Square are equal, and perpendicular bisectors of, One another. To construct the, Tequired square we will follow, the below given steps., , Step 1: Draw the rough sketch of, the required square ABCD., , Step 2: Draw a line segment AC of length 8 cm., Step 3: With the help of compass, construct a, Perpendicular bisector of the line segment AC. Mark, the point of intersection as O., , Rough shetel, , , , Step 4: With O as the centre and OA = 4 cm as the, radius, cut the perpendicular bisectors on cither side, of the line segment a2, , AC at Band D riN, Tespectively. F : =, Step 5: Join AB, BC,, , CD, and DA. A Oo. c, Hence, ABCD is the <<, , required square. Ry X, , (Note: Measure the _ ik:, lengths of AB, BC, NY, , CD, and DA. All of B, , these should be of cm, , same length.), , , , , , , 1. Construct a square PORS with PQ = 4 cm., 2. Construct a square DART with DR = 10 cm., , , , CONSTRUCTION OF A RECTANGLE, , The properties of a rectangle are:, , + Opposite sides of a rectangle are equal., , + Each angle ina P Ss, rectangle is a right Sie, angle., , + Diagonals are equal in et, length. : a, , With the help of these, , properties, let us construct a rectangle given only, specific dimensions., , , , A qjacent sides are Given, , oy. Construct a rectangle ABCD wig., , mand 4.cm- 4, , Sem i, , = cpzsemand —., m., , BC =DA= - line segment AB of length § cm, , step - with the help of a compass, construct ,, ep *, , st, , ndicular AX at, , imi with the help of a compass,, , ~—. Simi endicular BY at B., cone With ‘A and Bas centres and radius 4 cr, 4., ee which intersect the perpendiculars AX and Ps, DandC respectively:, Step 6: Join Cand D., Hence, ABCD x, is the requi |, rectangle with 2. it, adjacent sides, Scmand 4 cm. > as, , lote: Use the, ae cadcheck **™ |, whether CD is, Sem or not. If we PD, it is 5 cm, the A = ‘bb, construction is, correct), , Given One Side and a Diagonal, , Example 10; Construct a rectangle PQRS in which, side QR = 5 cm and diagonal QS = 6,2 cm., Solution:, , Step 1: Draw a rough sketch of, , , , P, rectangle PORS with QR=Sem = [777, and QS = 6.2 cm. Y, Step 2: Draw a line segment QR of vy, length 5 cm., Step 3: Construct a i, oe 7" eam ta, Step 4: With Q as centre and radius me, 6.2 cm draw an are, cutting RX at S., , oie Draw an are with Sas the centre and radius