Selina solutions concise mathematica class 7 icse Solutions for Chapter 15 triangles

Exercises in Chapter 15 triangles Grade 7

Exercise 15(A)

Exercise 15(B)

Exercise 15(C)

Questions in Exercise 15(A)

Q1) State if the triangles are possible with the following angles :

$(i)\ \ 20^{\circ},70^{\circ}and\ 90^{\circ}$

$(ii)\ 40^{\circ},130^{\circ}\ and\ 20^{\circ}$

$(iii)\ 60^{\circ},60^{\circ}\ and\ 50^{\circ}$

$(iv)\ 125^{\circ},40^{\circ}and\ 15^{\circ}$

Q2) If the angles of a triangle are equal, find its angles.

Q3) In a triangle ABC, ∠A = 45° and ∠B = 75°, find ∠C.

Q4) In a triangle QPR, ∠P = 60° and ∠Q = ∠R, find ∠R

Q5) Calculate the unknown marked angles in each figure:

Q6) Find the value of each angle in the given figures:

Q7) Find the unknown marked angles in the given figure:

Q8) In the given figure, show that: ∠a = ∠b + ∠c

(i) If ∠b = 60° and ∠c = 50° ; find ∠a.

(ii) If ∠a = 100° and ∠b = 55° : find ∠c.

(iii) If ∠a = 108° and ∠c = 48° ; find ∠b.

Q9) Calculate the angles of a triangle if they are in the ratio 4 : 5 : 6.

Q10) One angle of a triangle is 60°. The other two angles are in the ratio of 5: 7. Find the two angles.

Q11) One angle of a triangle is 61° and the other two angles are in the ratio $1\frac{1}{2}:1\frac{1}{3}.$ . Find these angles.

Q12) Find the unknown marked angles in the given figures :

Questions in Exercise 15(B)

Q1) Find the unknown angles in the given figures:

Q2) Apply the properties of isosceles and equilateral triangles to find the unknown angles in the given figures :

Q3) The angle of vertex of an isosceles triangle is 100°. Find its base angles.

Q4) One of the base angles of an isosceles triangle is 52°. Find its angle of the vertex.

Q5) In an isosceles triangle, each base angle is four times its vertical angle. Find all the angles of the triangle

Q6) The vertical angle of an isosceles triangle is 15° more than each of its base angles. Find each angle of the triangle.

Q7) The base angle of an isosceles triangle is 15° more than its vertical angle. Find its each angle.

Q8) The vertical angle of an isosceles triangle is three times the sum of its base angles. Find each angle.

Q9) The ratio between a base angle and the vertical angle of an isosceles triangle is 1 : 4. Find each angle of the triangle.

Q10) In the given figure, BI is the bisector of∠ABC and Cl is the bisector of ∠ACB. Find ∠BIC.

Q11) In the given figure, express a in terms of b.

Q12) (a) In Figure (i) BP bisects ABC and AB = AC. Find x.

(b) Find x in Figure (ii) Given: DA = DB = DC, BD bisects ABC andADB = 70°.

Q13) In each figure, given below, ABCD is a square and ∆ BEC is an equilateral triangle.

Find, in each case : (i) ∠ABE(ii) ∠BAE

Q14) In ∆ ABC, BA and BC are produced. Find the angles a and h. if AB = BC

Questions in Exercise 15(C)

Q1) Construct a ∆ABC such that:

(i) AB = 6 cm, BC = 4 cm and CA = 5.5 cm

(ii) CB = 6.5 cm, CA = 4.2 cm and BA = 51 cm

(iii) BC = 4 cm, AC = 5 cm and AB = 3.5 cm

Q2) Construct a A ABC such that:

(i) AB = 7 cm, BC = 5 cm and ∠ABC = 60°

(ii) BC = 6 cm, AC = 5.7 cm and ∠ACB = 75°

(iii) AB = 6.5 cm, AC = 5.8 cm and ∠A = 45°

Q3) Construct a ∆ PQR such that :

(i) PQ = 6 cm, ∠Q = 60° and ∠P = 45°. Measure ∠R.

(ii) QR = 4.4 cm, ∠R = 30° and ∠Q = 75°. Measure PQ and PR.

(iii) PR = 5.8 cm, ∠P = 60° and ∠R = 45°.

Measure ∠Q and verify it by calculations

Q5) Construct an isosceles ∆ABC such that:

(i) AB = AC = 6.5 cm and ∠A = 60°

(ii) One of the equal sides = 6 cm and vertex angle = 45°. Measure the base angles.

(iii) BC = AB = 5-8 cm and ZB = 30°. Measure ∠A and ∠C.

Q6) Construct an equilateral A ABC such that:

(i) AB = 5 cm. Draw the perpendicular bisectors of BC and AC. Let P be the point of intersection of these two bisectors. Measure PA, PB, and PC.

(ii) Each side is 6 cm.

Q7) (i) Construct a ∆ ABC such that AB = 6 cm, BC = 4.5 cm and AC = 5.5 cm. Construct a circumcircle of this triangle.

(ii) Construct an isosceles ∆PQR such that PQ = PR = 6.5 cm and ∠PQR = 75°. Using ruler and compasses only construct a circumcircle to this triangle.

(iii) Construct an equilateral triangle ABC such that its one side = 5.5 cm.

Construct a circumcircle to this triangle.

Q8) (i) Construct a ∆ABC such that AB = 6 cm, BC = 5.6 cm and CA = 6.5 cm. Inscribe a circle to this triangle and measure its radius.

(ii) Construct an isosceles ∆ MNP such that base MN = 5.8 cm, base angle MNP = 30°. Construct an incircle to this triangle and measure its radius.

(iii) Construct an equilateral ∆DEF whose one side is 5.5 cm. Construct an incircle to this triangle.

(iv) Construct a ∆ PQR such that PQ = 6 cm, ∠QPR = 45° and angle PQR = 60°. Locate its in centre and then draw its incircle.

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Chapters in this book

Integers

Rational Numbers

Fractions (Including Problems)

Decimal Fractions (Decimals)

Exponents (including Laws of Exponents)

Ratio and Proportion (Including Sharing in a Ratio)

Unitary Method (including Time and Work)

Percent and Percentage

Profit, Loss and Discount

Simple Interest

Fundamental Concepts (Including Fundamental Operations)

Simple Linear Equations (Including Word Problems)

Set Concepts (Some Simple Divisions by Vedic Method)

Lines and Angles (Including Construction of angles)

Triangles

Pythagoras Theorem

Symmetry (Including Reflection and Rotation)

Recognition of Solids (Representing 3-D in 2-D)

Congruency: Congruent Triangles

Mensuration

Data Handling

Probability