R d sharma mathematics solutions class 6 Solutions for Chapter 12 triangles

Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get? Name the triangle. Also, name

(i) the side opposite to ∠ B

(ii) the angle opposite to side AB

(iii) the vertex opposite to side BC

(iv) the side opposite to vertex B.

Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figurea triangle? If not, why?

Distinguish between a triangle and its triangular region

In Fig. 12.11, D is a point on side BC of a △ ABC. AD is joined. Name all the triangles that youcan observe in the figure. How many are they?

In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect atO. There are eight triangles that you can observe. Name all the triangles.

What is the difference between a triangle and triangular region?

Explain the following terms:

(i) Triangle

(ii) Parts or elements of a triangle

(iii) Scalene triangle

(iv) Isosceles triangle

(v) Equilateral triangle

(vi) Acute triangle

(vii) Right triangle

(viii) Obtuse triangle

(ix) Interior of a triangle

(x) Exterior of a triangle

In Fig. 12.13, the length (in cm) of each side has been indicated along the side. State for each triangle whether it is scalene, isosceles or equilateral.

In Fig. 12.14, there are five triangles. The measures of some of their angles have been indicated. State for each triangle whether it is acute, right or obtuse.

Fill in the blanks with the correct word/symbol to make it a true statement:

(i) A triangle has ……. sides.

(ii) A triangle has ………. verticals.

(iii) A triangle has ………. angles.

(iv) A triangle has ………. parts.

(v) A triangle whose no two sides are equal is known as ……..

(vi) A triangle whose two sides are equal is known as ……..

(vii) A triangle whose all the sides are equal is known as …….

(viii) A triangle whose one angle is a right angle is known as ……..

(ix) A triangle whose all the angles are of measures less than 90o is known as …….

(x) A triangle whose one angle is more than 90o is known as …….

In each of the following, state if the statement is true (T) or false (F):

(i) A triangle has three sides.

(ii) A triangle may have four vertices.

(iii) Any three line-segments make up a triangle.

(iv) The interior of a triangle includes its vertices.

(v) The triangular region includes the vertices of the corresponding triangle.

(vi) The vertices of a triangle are three collinear points.

(vii) An equilateral triangle is isosceles also.

(viii) Every right triangle is scalene.

(ix) Each acute triangle is equilateral.

(x) No isosceles triangle is obtuse.

In each of the following, state if the statement is true (T) or false (F): (i) A triangle has three sides. (ii) A triangle may have four vertices. (iii) Any three line-segments make up a triangle. (iv) The interior of a triangle includes its vertices. (v) The triangular region includes the vertices of the corresponding triangle. (vi) The vertices of a triangle are three collinear points.