Construction - Exercise 16.3 | Extra Documents & Tests for Class 9 PDF Download

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Question:19
Construct a ? ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ?B = 60°.
Solution:
We are asked to construct a triangle ABC in which , and
Page 2


            
                       
        
                     
                   
                  
                        
                 
 
 
            
                       
 
                     
 
                       
                        
                  
 
           
                      
                     
                   
                  
          
                   
                       
  
            
Question:19
Construct a ? ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ?B = 60°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.6 cm
STEP2: Draw .
STEP3: From ray BE, cut BD of 4.8 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:20
Construct a ? ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 4.5 cm.
STEP2: Draw 
STEP3: From ray BE, cut BD of 5.6 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Page 3


            
                       
        
                     
                   
                  
                        
                 
 
 
            
                       
 
                     
 
                       
                        
                  
 
           
                      
                     
                   
                  
          
                   
                       
  
            
Question:19
Construct a ? ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ?B = 60°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.6 cm
STEP2: Draw .
STEP3: From ray BE, cut BD of 4.8 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:20
Construct a ? ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 4.5 cm.
STEP2: Draw 
STEP3: From ray BE, cut BD of 5.6 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:21
Construct a ? ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.4 cm.
STEP2: Draw CBE = 
STEP3: From the ray BE, cut BD of 1.5 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw AC.
?ABC is the required angle.
Question:22
Using ruler and compasses only, construct a ?ABC, given base BC = 7 cm, ?ABC = 60° and AB + AC = 12 cm.
Solution:
We are asked to construct a triangle ABC in which BC = 7 cm, ?B = 60° and AB  + AC = 12 cm
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of length 7 cm.
STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.
STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.
Page 4


            
                       
        
                     
                   
                  
                        
                 
 
 
            
                       
 
                     
 
                       
                        
                  
 
           
                      
                     
                   
                  
          
                   
                       
  
            
Question:19
Construct a ? ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ?B = 60°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.6 cm
STEP2: Draw .
STEP3: From ray BE, cut BD of 4.8 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:20
Construct a ? ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 4.5 cm.
STEP2: Draw 
STEP3: From ray BE, cut BD of 5.6 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:21
Construct a ? ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.4 cm.
STEP2: Draw CBE = 
STEP3: From the ray BE, cut BD of 1.5 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw AC.
?ABC is the required angle.
Question:22
Using ruler and compasses only, construct a ?ABC, given base BC = 7 cm, ?ABC = 60° and AB + AC = 12 cm.
Solution:
We are asked to construct a triangle ABC in which BC = 7 cm, ?B = 60° and AB  + AC = 12 cm
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of length 7 cm.
STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.
STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.
STEP4: Draw BM and produce it to P.
STEP5: From BP, cut BR = 12 cm.
STEP6: Draw segment RC.
STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.
STEP8: Draw AC.
?ABC is the required triangle.
Question:23
Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60°.
Solution:
We are asked to draw triangle ABC whose base angles are 60
° and 90°
 and its perimeter is 10 cm.
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw a line segment DE of 10 cm.
STEP2: Draw ?EDM = ?B = 90° and ?DEN = ?C = 60°.
STEP3: Draw the angle bisectors of ?EDM and ?DEN and mark their point of intersection as A.
STEP4: Draw the perpendicular bisectors of AD and AE. They meet DE at B and C respectively.
STEP5: Draw AB and AC to get the desired ?ABC.
Question:24
Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.
Solution:
We are given and median 
We have to construct the triangle ABC
We will follow the following algorithm for the construction
Page 5


            
                       
        
                     
                   
                  
                        
                 
 
 
            
                       
 
                     
 
                       
                        
                  
 
           
                      
                     
                   
                  
          
                   
                       
  
            
Question:19
Construct a ? ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ?B = 60°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.6 cm
STEP2: Draw .
STEP3: From ray BE, cut BD of 4.8 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:20
Construct a ? ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 4.5 cm.
STEP2: Draw 
STEP3: From ray BE, cut BD of 5.6 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw segment AC.
?ABC is the required angle.
Question:21
Construct a ? ABC in which BC = 3.4 cm, AB - AC = 1.5 cm and ?B = 45°.
Solution:
We are asked to construct a triangle ABC in which , and
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of 3.4 cm.
STEP2: Draw CBE = 
STEP3: From the ray BE, cut BD of 1.5 cm.
STEP4: Draw segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A
STEP6: Draw AC.
?ABC is the required angle.
Question:22
Using ruler and compasses only, construct a ?ABC, given base BC = 7 cm, ?ABC = 60° and AB + AC = 12 cm.
Solution:
We are asked to construct a triangle ABC in which BC = 7 cm, ?B = 60° and AB  + AC = 12 cm
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw BC of length 7 cm.
STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.
STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.
STEP4: Draw BM and produce it to P.
STEP5: From BP, cut BR = 12 cm.
STEP6: Draw segment RC.
STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.
STEP8: Draw AC.
?ABC is the required triangle.
Question:23
Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60°.
Solution:
We are asked to draw triangle ABC whose base angles are 60
° and 90°
 and its perimeter is 10 cm.
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw a line segment DE of 10 cm.
STEP2: Draw ?EDM = ?B = 90° and ?DEN = ?C = 60°.
STEP3: Draw the angle bisectors of ?EDM and ?DEN and mark their point of intersection as A.
STEP4: Draw the perpendicular bisectors of AD and AE. They meet DE at B and C respectively.
STEP5: Draw AB and AC to get the desired ?ABC.
Question:24
Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.
Solution:
We are given and median 
We have to construct the triangle ABC
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw a line segment BC of length 6 cm.
STEP2: Draw the perpendicular bisector of line BC cutting the line at point D, such that BD = 3 cm.
STEP3: With centre B and radius = 6 cm, draw an arc.
STEP4: With centre D and radius = 4 cm, draw an arc intersecting the previous arc at A.
STEP5: Draw AC to get the desired ?ABC.
Question:25
Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.
Solution:
We have to construct a right triangle ABC with base and the sum of hypotenuse and the other side is 10
cm
We will follow the following algorithm for the construction
Steps of construction
STEP1: Draw a line segment BC of length 6 cm.
STEP2: Draw CBE = 
STEP3: From BE, cut BD of length 10 cm.
STEP4: Draw the line segment DC.
STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at point A
STEP6: Draw AC to get the desired ?ABC.