Mathematics · Textbook solutions

Constructions of Triangles

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 18 questions

Construction I

1 q

Solved Examples

Worked · 1
  1. 4.1 SolvedEx.1
    Construct △ABC\triangle ABC in which BC=6.3BC = 6.3 cm, ∠B=75∘\angle B = 75^\circ and AB+AC=9AB + AC = 9 cm.

Practice Set 4.1

4 q
  1. Ex 4.1 Q1
    Construct △PQR\triangle PQR, in which QR=4.2QR = 4.2 cm, m∠Q=40∘m\angle Q = 40^\circ and PQ+PR=8.5PQ + PR = 8.5 cm.
  2. Ex 4.1 Q2
    Construct △XYZ\triangle XYZ, in which YZ=6YZ = 6 cm, XY+XZ=9XY + XZ = 9 cm, ∠XYZ=50∘\angle XYZ = 50^\circ.
  3. Ex 4.1 Q3
    Construct △ABC\triangle ABC, in which BC=6.2BC = 6.2 cm, ∠ACB=50∘\angle ACB = 50^\circ, AB+AC=9.8AB + AC = 9.8 cm.
  4. Ex 4.1 Q4
    Construct △ABC\triangle ABC, in which BC=3.2BC = 3.2 cm, ∠ACB=45∘\angle ACB = 45^\circ and perimeter of △ABC\triangle ABC is 10 cm.

Construction II

2 q

Solved Examples

Worked · 2
  1. 4.2 SolvedEx.1
    Construct △ABC\triangle ABC, such that BC=7.5BC = 7.5 cm, ∠ABC=40∘\angle ABC = 40^\circ, AB−AC=3AB - AC = 3 cm.
  2. 4.2 SolvedEx.2
    Construct △ABC\triangle ABC, in which side BC=7BC = 7 cm, ∠B=40∘\angle B = 40^\circ and AC−AB=3AC - AB = 3 cm.

Practice Set 4.2

3 q
  1. Ex 4.2 Q1
    Construct △XYZ\triangle XYZ, such that YZ=7.4YZ = 7.4 cm, ∠XYZ=45∘\angle XYZ = 45^\circ and XY−XZ=2.7XY - XZ = 2.7 cm.
  2. Ex 4.2 Q2
    Construct △PQR\triangle PQR, such that QR=6.5QR = 6.5 cm, ∠PQR=40∘\angle PQR = 40^\circ and PQ−PR=2.5PQ - PR = 2.5 cm.
  3. Ex 4.2 Q3
    Construct △ABC\triangle ABC, such that BC=6BC = 6 cm, ∠ABC=100∘\angle ABC = 100^\circ and AC−AB=2.5AC - AB = 2.5 cm.

Construction III

1 q

Solved Examples

Worked · 1
  1. 4.3 SolvedEx.1
    Construct △ABC\triangle ABC such that AB+BC+CA=11.3AB + BC + CA = 11.3 cm, ∠B=70∘\angle B = 70^\circ, ∠C=60∘\angle C = 60^\circ.

Practice Set 4.3

3 q
  1. Ex 4.3 Q1
    Construct △PQR\triangle PQR, in which ∠Q=70∘\angle Q = 70^\circ, ∠R=80∘\angle R = 80^\circ and PQ+QR+PR=9.5PQ + QR + PR = 9.5 cm.
  2. Ex 4.3 Q2
    Construct △XYZ\triangle XYZ, in which ∠Y=58∘\angle Y = 58^\circ, ∠X=46∘\angle X = 46^\circ and perimeter of triangle is 10.5 cm.
  3. Ex 4.3 Q3
    Construct △LMN\triangle LMN, in which ∠M=60∘\angle M = 60^\circ, ∠N=80∘\angle N = 80^\circ and LM+MN+NL=11LM + MN + NL = 11 cm.

Problem Set 4

4 q
  1. Prob Q1
    Construct △XYZ\triangle XYZ, such that XY+XZ=10.3XY + XZ = 10.3 cm, YZ=4.9YZ = 4.9 cm, ∠XYZ=45∘\angle XYZ = 45^\circ.
  2. Prob Q2
    Construct △ABC\triangle ABC, in which ∠B=70∘\angle B = 70^\circ, ∠C=60∘\angle C = 60^\circ, AB+BC+AC=11.2AB + BC + AC = 11.2 cm.
  3. Prob Q3
    The perimeter of a triangle is 14.4 cm and the ratio of lengths of its side is 2:3:42 : 3 : 4. Construct the triangle.
  4. Prob Q4
    Construct △PQR\triangle PQR, in which PQ−PR=2.4PQ - PR = 2.4 cm, QR=6.4QR = 6.4 cm and ∠PQR=55∘\angle PQR = 55^\circ.