Selina solutions concise mathematics class 6 icse Solutions for Chapter 26 triangles including types properties and construction

Exercises in Chapter 26 triangles including types properties and construction Grade 6

Exercise 26(A)

Exercise 26(B)

Revision Exercise

Questions in Exercise 26(A)

Q1) In each of the following, find the marked unknown angles :

Q2) Can a triangle together have the following angles ?

(i) 55°, 55° and 80° (ii) 33°, 74° and 73° (iii) 85°, 95° and 22°.

Q3) Find x, if the angles of a triangle are:

(i) x°, x°, x°

(ii) x°, 2x°, 2x°

(iii) 2x°, 4x°, 6x°

Q4) One angle of a right-angled triangle is 70°. Find the other acute angle.

Q5) In ∆ABC, ∠A = ∠B = 62° ; find ∠C.

Q6) In ∆ABC, C = 56°C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.

Q7) Find, giving reasons, the unknown marked angles, in each triangle drawn below:

Q8) Classify the following triangles according to angle :

Q9) Classify the following triangles according to sides :

Questions in Exercise 26(B)

Q1) Construct triangle ABC when:

AB = 6 cm, BC = 8 cm and AC = 4 cm.

Q2) Construct triangle ABC, when :

AB = 3.5 cm, AC = 4.8 cm and BC = 5.2 cm.

Q3)Construct triangle ABC, when :

AB = BC = 5 cm and AC = 3 cm. Mea¬sure angles A and C. Is ∠A = ∠C?

Q4) Construct triangle ABC, when :

AB = BC = CA = 4.5 cm. Measure all the angles of the triangle. Are they equal ?

Q5) Construct triangle ABC, when :

AB = 3 cm, BC = 7 cm and ∠B = 90°.

Q6) Construct triangle ABC, when :

AC = 4.5 cm, BC = 6 cm and ∠C = 60°.

Q7) Construct triangle ABC, when :

AC = 6 cm, ∠A = 60“ and ∠C = 45°. Measure AB and BC.

Q8) Construct triangle ABC, when :

AB = 5.4 cm, ∠A = 30° and ∠B = 90°. Measure ∠C and side BC.

Q9) Construct triangle ABC, when :

AB = 7 cm, ∠B = 120° and ∠A = 30°. Measure AC and BC.

Q10) Construct triangle ABC, when :

BC = 3 cm, AC = 4 cm and AB = 5 cm. Measure angle ACB. Give a special name to this triangle.

Questions in Revision Exercise

Q1) If each of the two equal angles of an isosceles triangle is 68°, find the third angle.

Q2) One of the angles of a triangle is 110°, the two other angles are equal. Find their value.

Q3) The angles of a triangle are in the ratio 3 : 5 : 7. Find each angle.

Q4) The angles of a triangle are (2x – 30°),(3x – 40°) and $\frac{5}{2}x+10^{\circ}$ Find the value of x .

Q5) In each of the following figures, triangle ABC is equilateral and triangle PBC is isosceles. If PBA = 20°; find in each case:

(a) angle PBC.

(b) angle BPC.

Q6) Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.

Q7) Construct a triangle PQR, given PQ = 6 cm, ∠P = 60° and ∠Q = 30°. Measure angle R and the length of PR.

Q8) Construct a triangle ABC given BC = 5 cm, AC = 6 cm and ∠C = 75°. Draw the bisector of the interior angle at A. Let this bisector meet BC at P ; measure BP.

Q9) Using ruler and a pair compass only, construct a triangle XYZ given YZ = 7 cm, ∠XYZ = 60° and ∠XZY = 45°. Draw the bisectors of angles X and Y.

Q10) Using ruler and a pair compass only, construct a triangle PQR, given PQ = 5.5 cm, QR = 7.5 cm and RP = 6 cm. Draw the bisectors of the interior angles at P, Q and R. Do these bisectors meet at the same point ?

Q11) One angle of a triangle is 80° and the other two are in the ratio 3 : 2. Find the unknown angles of the triangle.