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ICSE Prelims 2018 : Chemistry (St. Francis School, North 24 Parganas)

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Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Exercise 17.1 1. Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part. Sol: Steps of construction: 1. Draw a line segment AB of 8 6cm 1 AB , draw arcs, one on each side of AB 2 3. With center B and same radius, draw arcs cutting the previous arcs at P and Q respectively 4. Join PQ 2. With center A and radius more than n AC BC 4 3cm 2. Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment. Sol: Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Steps of construction: 1. Draw a line segment AB of 5 8cm 1 AB , draw arcs with one on each side of AB 2 3. With center B and same radius draw arcs cutting the previous arcs at P and Q respectively. 4. Join PQ Hence, PQ is the perpendicular bisector of AB. 2. With center A and radius more than 3. Draw a circle with centre at point O and radius 5 cm. Draw its chord AB, draw the perpendicular bisector of line segment AB. Does it pass through the centre of the circle? Sol: Steps of construction: 1. With center O and radius 5cm draw a circle 2. Draw a chord AB. 1 3. With center A and radius more than AB , draw arcs one on each side of 2 4. With center B and same radius draw arcs cutting previous arcs at P and Q respectively. 5. Join PQ yes perpendicular bisector PQ of AB passes through center of the circle. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 4. Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect? Sol: Steps of construction: 1. With center O and any radius, draw a circle 2. Draw two chords AB and CD. 1 3. With center A and radius more than AB , draw arcs, one on each side of AB 2 4. With center B and same radius draw arcs cutting previous arcs at P and Q respectively. 5. Join PQ 1 6. With center D and radius more than DC . draw arcs, one on each side of DC 2 7. With center C and same radius, draw arcs cutting previous arcs at R and S respectively 8. Join RS Both perpendicular bisector PQ and RS intersect each other at the center O of he circle. 5. Draw a line segment of length 10 cm and bisect it. Further bisect one of the equal parts and measure its length. Sol: Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Steps of construction: 1. Draw a line segment AB of 10cm 1 AB , draw arcs one on each side of AB 2 3. With center B and same radius draw arcs cutting previous arcs at P and Q respectively. 4. Join PQ and which intersect AB at C 1 5. With center A and radius more than AC , drawing on each side of AC. 2 6. With center C and same radius, draw arcs cutting previous arcs at R and S respectively. 7. Join RS and which intersect AC at b. 2. With center A and radius more than AD 2 5cm. 6. Draw a line segment AB and bisect it. Bisect one of the equal parts to obtain a line segment 1 of length (AB). 2 Sol: Steps of construction: 1. Draw a line segment AB 1 AB , draw arcs one on each side of AB 2 3. With center B and same radius draw arcs cutting previous arcs at P and Q respectively. 4. Join PQ and which intersect AB at C 1 5. With center A and radius more than AC , draw arcs, one on each side of AC. 2 2. With center A and radius more than Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 6. With center C and same radius, draw arcs cutting previous arcs at R and S respectively. 7. Join RS and which intersect AC at D 1 AD AB. 4 7. Draw a line segment AB and by ruler and compasses1 obtain a line segment of length 3 AB . 4 Sol: Steps of construction: 1. Draw a line segment AB 1 AB , draw arcs one on each side of AB. 2 3. With center B and same radius draw arcs cutting previous arcs at P and Q respectively. 4. Join PQ and which intersect AB at C 1 5. With center C and radius more than CB , draw arcs, one on each side of CB. 2 6. With center B and same radius, draw arcs cutting previous arcs at R and S respectively. 7. Join RS and which intersect CB at D 3 AD AB. 4 2. With center A and radius more than Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Exercise 17.2 1. Draw an angle and label it as BAC. Construct another angle, equal to BAC. Sol: Steps of construction: 1. Draw an angle ABO and a Line segment QR 2. With center A and any radius, draw an arc which intersects BAC at E and O 3. With center Q and same radius draw arc which intersect QR at S. 4. With center S and radius equal to DE, draw an arc which intersect previous arc at T 5. Draw a line segment joining Q and T PQR BAC 2. Draw an obtuse angle, Bisect it. Measure each of the angles so obtained. Sol: Steps of construction: 1. Draw angle ABC of 120 2. With center B and any radius, draw an arc which intersects AB at P and BC at Q 1 3. With center P and Q and radius more than PQ, draw two arcs, with intersect each other 2 at R. 4. Join BR ABR RBC 60 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 3. Using your protractor, draw an angle of measure 108 . With this angle as given, draw an angle of 54 . Sol: Steps of construction: 1. Draw an angle ABC of 108 2. With center B and any radius, draw an arc which intersects AB at P and BC at Q 1 3. With center P and Q and radius more than PQ, draw two arcs, which intersect each 2 other at R. 4. Join BR RBC 54 4. Using protractor, draw a right angle. Bisect it to get an angle of measure 45 . Sol: Steps of construction: 1. Draw an angle ABC of 90 2. With center B and any radius, draw an arc which intersects AB at P and BC at Q 1 3. With center P and Q and radius more than PQ, draw two arcs, which intersect each 2 other at R. 4. Join RB RBC 45 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 5. Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other. Sol: Steps of construction: 1. Draw two angle DCA and DCB forming Linear pair 2. With center C and any radius, draw an arc which intersects AC at P, CD at Q and CB at R. 3. With center P and Q and any radius draw two arcs which interest each other at S 4. Join SC 5. With center Q and R any radius draw two arcs, which intersect each other at T. 6. Join TC [By using protractor] SCT 90 6. Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line. Sol: Steps of construction: 1. Draw a pair of vertically opposite angle AOC and DOB 2. With center O and any radius drawn two arcs which intersect OA at P, Q OB at S and OD at R. 1 3. With center P and Q and radius more than PQ, draw two arcs which intersect each 2 other at 7. 4. Join to Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 5. With center R and S radius more than 1 RS , draw two arcs which intersect each other at 2 U. 6. Join OU. TOU is a straight line 7. Using ruler and compasses only, draw a right angle. Sol: Steps of construction: 1. Draw a line segment AB 2. With center A and any radius draw arc which intersect AB at C. 3. With center C and same radius draw an arc which intersects AB at C. 4. With center D and same radius draw arc which intersect arc in (2) at E. 5. With centers E and C and any radius, draw two arcs which intersect each other at F. 6. Join FA FAB 90 8. Using ruler and compasses only, draw an angle of measure 135 . Sol: Steps of construction: 1. Draw a line segment AB and produce BA to point C. 2. With center A and any radius draw arc which intersect AC at D and AB at E. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 3. With center D and E and radius more than 1 DE , draw two arcs which intersect each 2 other at F. 4. Join FA which intersect the arc in (2) at G. 5. With centers G and D and radius more than 1 GD, draw two arcs which intersect each 2 other at H. 6. Join HA HAB 135 9. Using a protractor, draw an angle of measure 72 . With this angle as given, draw angles of measure 36 and 54 . Sol: Steps of construction: 1. Draw an angle ABC of 72 with the help of protractor. 2. With center B and any radius, draw an arc which intersect AB at D and BC at E. 1 3. With center D and E and radius more than DE , draw two arcs which intersect each 2 other at F. 4. Join FB which intersect the arc in (2) at G. 1 5. With centers D and G and radius more than DE , draw two arcs which intersect each 2 other at F. 1 6. With centers D and G and radius more than n DG draw two arcs which intersect each 2 other at H 7. Join HB HBC 54 FBC 36 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 10. Construct the following angles at the initial point of a given ray and justify the construction: (i) 45 (ii) 90 Sol: (i) Steps of construction: 1. Draw a line segment AB and produce BA to point C. 2. With center A and any radius drawn an arc which intersect AC at D and AB at E. 1 3. With center D and E and radius more than DE , draw arcs cutting each other at F. 2 4. Join FA which intersect arc in (2) at G. 1 5. With centers G and E and radius more than GE , draw arcs cutting each other at H. 2 6. Join HA HAB 45 (ii) Steps of construction: 1. Draw a line segment AB. 2. With center A and any radius draw in arc which intersect AB at C. 3. With center C and same radius draw an arc which intersects previous arc at D. 4. With centers D same radius draw an arc which intersects are in (2) at E. 1 5. With centers E and D same radius more than ED draw an arc cutting each other at F. 2 6. Join FA FAB 90 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 11. Construct the angles of the following measurements: (i) 30 (ii) 75 (iii) 105 (iv) 135 (v) 15 (vi) 22 1 2 Sol: (i) Steps of construction: 1. Draw a line segment AB. 2. With center A and any radius, draw an arc which intersect AB at C. 3. With center C and same radius, draw an arc which intersects previous arc at D. 1 4. With centers D and C and radius more than DC , draw arcs intersecting each other at 2 E 5. Join EA EAB 30 (ii) Steps of construction: 1. Draw a line segment AB. 2. With center A any radius, draw an arc which intersect AB at C. 3. With center C and same radius, draw an arc which intersects previous arc at D. 4. With center D and same radius, draw an arc which interest are in (2) at E 1 5. With centers E and D and radius more than ED, draw arcs intersecting each other at 2 F. 6. Join FA which intersects arc in (2) at G Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 7. With centers G and D, and radius more than 1 GD, draw arcs intersecting each other at 2 H. 8. Join HA HAB 75 (iii) Steps of construction: 1. Draw a line segment AB. 2. With center A and any radius, draw an arc which intersect AB at C. 3. With center C and same radius, draw an arc which intersects previous arc at D. 4. With center D and same radius, draw an arc which interest are in (2) at E 1 5. With centers E and D and radius more than ED, draw arcs intersecting each other at 2 F. 6. Join FA which intersects arc in (2) at E 7. With centers E and G, and radius more than half of EG, draw arcs intersecting each other at H. 8. Join HA HAB 105 (iv) Steps of construction: 1. Draw a line segment AB and produce BA to pint C 2. With center A and any radius, draw an arc which intersect AC to D and AB at E. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 3. With center D and E and radius more than half of DE, draw two arcs which intersects each other at F. 4. Join FA which intersect the arc in (2) at G 1 5. With center G and D radius more than GD, draw two arcs which intersect each other 2 at H 6. Join HA HAB 135 (v) Steps of construction: Step 1: Draw a line segment AB Step 2: with center A and any radius, draw an arc which intersects previous arc at C Step 3: with center C and same radius, draw an arc which intersect previous arc at D Step 4: with center D and C radius more than half of DC draw arcs intersecting each other at E Step 5: Join EA which intersects arc in (2) at F. 1 Step 6: With centers F and C and radius more than FC , draw arcs intersecting each other 2 Step 7: Join GA GAB 15 (vi) Steps of construction: Step 1: Draw a line segment AB Step 2: with center A and any radius, draw an arc which intersects AB at C Step 3: with center C and same radius, draw an arc which intersect previous arc at D Step 4: with center D and same radius, draw an arc which intersects arc in (2) at E. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Step 5: with center E and D and radius more than half of ED, draw arcs intersecting each other at F. Step 6: Join FA which intersects arc in (2) at G Step 7: with center G and C and radius more than half of GC, draw arcs intersecting each other at H Step 8: Join HA which intersects arc in (2) at 1. Step 9: with centers I and C and radius more than half of IC, draw arcs intersecting each other Step 10: Join JA 1 JAB 22 . 2 Exercise 17.3 1. Construct a ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and B = 60 . Sol: Steps of construction: 1. Draw a line segment BC of 3 6 cm. 2. At the point B, draw x BC of 60 3. With center B and radius 4 8cm, draw an arc which intersects XB at D. 4. Join DC 5. Draw the perpendicular bisector of DC which intersects DB at A. 6. Join AC Hence ABC is the required triangle Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 2. Construct a ABC in which AB + AC = 5.6 cm, BC = 4.5 cm, AB AC = 1.5 cm and B = 45 . Sol: Steps of construction: Step 1: Draw a line segment BC of 4 5cm. Step 2: At B, draw an angle XBC of 45 Step 3: With center B and radius 5 6cm, draw an arc which intersects BX at D. Step 4: Join DC Step 5: Draw the perpendicular bisector of DC which intersects BD at A. Step 6: Join AC ABC is a required triangle 3. Construct a ABC in which BC = 3.4 cm, AB AC = 1.5 cm and B = 45 . Sol: Steps of construction: Step 1: Draw a line segment BC of 3 5cm. Step 2: At B, draw an angle XBC of 45 Step 3: With center B and radius 1 5cm, draw an arc which intersects BX at D. Step 4: Join DC Step 5: Draw the perpendicular bisector of DC which intersects BD produced at A. Step 6: Join AC ABC is the required triangle Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 4. Using ruler and compasses only, construct a ABC, given base BC = 7cm, ABC = 60 and AB + AC = 12 cm. Sol: Steps of construction: 1. Draw a line segment BC of 7 cm. At B, draw an angle XBC of 60 With center B and radius 12cm, draw an arc which intersects BX at D. Join DC Draw the perpendicular bisector of DC which intersects BD at A. Join AC ABC is the required triangle. 2. 3. 4. 5. 6. 5. Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60 and 45 . Sol: Steps of construction: 1. Draw a line segment XY of 6 4cm. 2. Draw DXY B 60 and EYX C 45 3. Draw the angle bisector of DXY and EYX which interest each other at A. 4. Draw the perpendicular bisector of AX and AY which interest XY at B and C respectively. 5. Join AB and AC ABC is the required triangle. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ 6. Using ruler and compasses only, construct a ABC from the following data: AB + BC + CA = 12 cm, B = 45 and C = 60 . Sol: Steps of construction: Step 1: Draw a line segment XY of 12cm. Step 2: Draw DXY B 45 and EYX C 60 Step 3: Draw the angle bisectors of angles of DXY and EYX which intersects each other at A. Step 4: Draw the perpendicular of AX and AY which intersect XY at B and C respectively. Step 5: Join AB and AC ABC is the required triangle 7. Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60 . Sol: Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Steps of construction: Step 1: Draw a line segment XY of 10cm. Step 2: Draw DXY B 90 and FYX C 60 Step 3: Draw the angle bisectors of DXY and EYX which intersects each other at A. Step 4: Draw the perpendicular of AX and AY which intersect XY at B and C respectively. Step 5: Join AB and AC ABC is the required triangle 8. Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm. Sol: Steps of construction: Step 1: Draw a line segment BC of 6cm. Step 2: Take midpoint D of BC. Step 3: with center B and D and radii 6cm and 4cm draw two arcs which intersects each other A Step 4: Join AB, AD and AC ABC is the required triangle 9. Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm. Sol: Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor. Class IX Chapter 17 Constructions Maths ______________________________________________________________________________ Steps of construction: Step 1: Draw a line segment BC of 6cm. Step 2: At B draw an angle le BC of 90 . Step 3: with center B and radius 10cm draw an arc which intersects XB at D. Step 4: Join DC. Step 5: Draw the perpendicular bisector of DC which intersects DB at A Step 6: Join AC ABC is the required triangle 10. Construct a triangle XYZ in which Y = 30 , Z = 90 and XY + YZ + ZX = 11. Sol: Steps of construction: Step 1: Draw a line segment AB of 11cm. Step 2: Draw DAB Y 30 and FBA Z 90 Step 3: Draw the angle bisector of DAB and EBA which intersect each other at x Step 4: Draw the perpendicular bisector XA and XB which intersect AB at Y and Z respectively. Step 5: Join XY and XZ XYZ is the required triangle Printed from Vedantu.com. 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