Exercise 12.1
Question 1: 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.
Solution 1: Take Three non-collinear points A, B and C, join them AB, BC and CD and we get a triangle △ABC.
(i) The side opposite to ∠ B is AC.
(ii) The angle opposite to side AB is ∠C.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
Question 2: Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a triangle? If not, why?
Solution 2: Consider A, B and C as three collinear points and join by line AB, BC and CA.
We get a straight line after join A, B and C because it has only one side and not a triangle. The straight line is not a closed figure whereas the triangle is a closed figure which has three sides.
Question 3: Distinguish between a triangle and its triangular region.
Solution 3:
Triangle: The triangle is formed by three points join with line segment, and defined as a plane figure which are non-parallel
Triangular Region: A triangular region is the region which is inside a triangle.
The figure represents a triangle with a triangular region which is shaded.
Question 4: In Fig. 12.11, D is a point on side BC of a △ ABC. AD is joined. Name all the triangles that you can observe in the figure. How many are they?
Solution 4: According to the given figure there are three triangles namely, △ ACD, △ ADB and △ ABC.
Question 5: In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O. There are eight triangles that you can observe. Name all the triangles.
Solution 5: The triangles which are present in the figure are △ ABC, △ ABD, △ ABO, △ BCO, △ DCO, △ AOD, △ ACD and △ BCD. There are about eight triangles which are present in the figure.
Question 6: What is the difference between a triangle and triangular region?
Solution 6: Triangle: The triangle is formed by three points join with line segment, and defined as a plane figure which are non-parallel
Triangular Region: A triangular region is the region which is inside a triangle.
The figure represents a triangle with a triangular region which is shaded.
Question 7:. 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.
Solution 7:
Question 8: 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.
Solution 8:
Question 9: 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.
Solution 9:
Question 10: 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 _______ .
Solution 10:
(i) A triangle has three sides.
(ii) A triangle has three verticals.
(iii) A triangle has three angles.
(iv) A triangle has six parts.
(v) A triangle whose no two sides are equal is known as scalene.
(vi) A triangle whose two sides are equal is known as isosceles.
(vii) A triangle whose all the sides are equal is known as equilateral.
(viii) A triangle whose one angle is a right angle is known as right triangle.
(ix) A triangle whose all the angles are of measures less than 90o is known as acute triangle.
(x) A triangle whose one angle is more than 90o is known as obtuse triangle.
Question 11: 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.
Solution 11:
Objective Type Questions ::->
Question 1: Total number of parts of a triangle is
(a) 3
(b) 6
(c) 9
(d) 1
Solution 1: The correct answer is (b).
Total number of parts of a triangle is 6, three vertex and three edges.
Question 2: A perpendicular drawn from a vertex to the opposite side of a triangle is known as
(a) an altitude
(b) a median
(c) an angle bisector
(d) a bisector
Solution 2: The correct answer is (a).
A perpendicular drawn from a vertex to the opposite side of a triangle is known as an altitude.
Question 3: A triangle
(a) may not have an altitude
(b) can have at most 3 altitudes
(c) has three altitudes
(d) has only one altitude
Solution 3: The correct answer is (c).
A triangle has three altitudes.
Question 4: Line segments joining the vertices to the mid-points of the opposite sides of a triangle are known as
(a) medians
(b) altitudes
(c) heights
(d) angle bisectors
Solution 4: The correct answer is (a).
Line segments joining the vertices to the mid-points of the opposite sides of a triangle are known as medians.
Question 5: A triangle whose no two sides are equal is known as
(a) an acute triangle
(b) a scalene triangle
(c) an isosceles triangle
(d) an equilateral triangle
Solution 5: The correct answer is (b).
A triangle whose no two sides are equal is known as a scalene triangle.
Question 6: A triangle whose two sides are equal is known as
(a) acute triangle
(b) an isosceles triangle
(c) a scalene triangle
(d) an isosceles triangle
Solution 6: The correct answer is (b).
A triangle whose two sides are equal is known as an isosceles triangle.
Question 7: A triangle whose all sides are equal is called
(a) an equilateral triangle
(b) an acute triangle
(c) a right triangle
(d) an isosceles triangle
Solution 7: The correct answer is (a).
A triangle whose all sides are equal is called an equilateral triangle.
Question 8: The sum of the length of sides of a triangle is known as its
(a) area
(b) height
(c) perimeter
(d) region
Solution 8: The correct answer is (c).
The sum of the length of sides of a triangle is known as its perimeter.
Question 9: A triangle having all sides of different length is known as
(a) scalene triangle
(b) isosceles triangle
(c) an equilateral triangle
(d) an acute triangle
Solution 9: The correct answer is (a).
A triangle having all sides of different length is known as scalene triangle.
Question 10: A triangle whose one angle is more than 90° is called
(a) a scalene triangle
(b) a right triangle
(c) an acute triangle
(d) an obtuse triangle
Solution 10: The correct answer is (d).
A triangle whose one angle is more than 90° is called an obtuse triangle.