0

Guest

Courses New
Book a free demo of live class

Constructions Exercise 17.4

Question: 1

Construct ∆ABC in which BC = 4 cm, ∠B = 50° and ∠C = 70°.

Solution:

Constructions Exercise 17.4 Question: 1

Steps of construction:

  • Draw a line segment BC of length 4 cm.

  • Draw ∠CBX such that ∠CBX=50°.

  • Draw ∠BCY with Y on the same side of BC as X such that ∠BCY=70°.

  • Let CY and BX intersect at A.

  • ABC is the required triangle.
     

Question: 2

Draw ∆ABC in which BC = 8 cm, ∠B = 50° and ∠A = 50°.

∠ABC + ∠BCA + ∠CAB = 180°

∠BCA = 180° − ∠CAB − ∠ABC

∠BCA = 180°− 100° = 80°

Solution:

Constructions Exercise 17.4 Question: 2

Steps of construction:

  • Draw a line segment BC of length 8 cm.

  • Draw ∠CBX such that ∠CBX = 50°.

  • Draw ∠BCY with Y on the same side of BC as X such that ∠BCY = 80°.

  • Let CY and BX intersect at A.
     

Question: 3

Draw ∆ABC in which ∠Q = 80°, ∠R = 55° and QR = 4.5 cm. Draw the perpendicular bisector of side QR.

Solution:

Constructions Exercise 17.4 Question: 3

Steps of construction:

  • Draw a line segment QR = 4.5 cm.

  • Draw ∠RQX = 80° and ∠QRY = 55°.

  • Let QX and RY intersect at P so that PQR is the required triangle.

  • With Q as centre and radius more that 2.25 cm, draw arcs on either sides of QR.

  • With R as centre and radius more than 2.25 cm, draw arcs intersecting the previous arcs at M and N.

  • Join MN

MN is the required perpendicular bisector of QR.

 

Question: 4

Construct ∆ABC in which AB = 6.4 cm, ∠A = 45° and ∠B = 60°

Solution:

Constructions Exercise 17.4 Question: 4

Steps of construction:

Draw a line segment AB = 6.4 cm.

Draw ∠BAX = 45°.

Draw ∠ABY with Y on the same side of AB as X such that ∠ABY = 60°.

Let AX and BY intersect at C.

ABC is the required triangle.

 

Question: 5

Draw ∆ABC in which AC = 6 cm, ∠A = 90° and ∠B = 60°.

∠A + ∠B + ∠C = 180°

Therefore ∠C = 180°− 60°− 90°= 30°

Solution:

Constructions Exercise 17.4 Question: 5

Steps of construction:

  • Draw a line segment AC = 6 cm.

  • Draw ∠ACX = 30°.

  • Draw ∠CAY with Y on the same side of AC as X such that ∠CAY = 90°.

  • Join CX and AY. Let these intersect at B.

ABC is the required triangle where angle ∠ABC = 60°.


TOP Your EXAMS!

Upto 50% Scholarship on Live Classes

Course Features

  • Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Book a Live class Live courses Ask question
r