**Understanding Elementary Shapes**

Exercise 5.6

1). Name the types of following triangles:

(a). Triangles with lengths of sides 7 cm, 8 cm and 9 cm.

(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(c). ∆PQR such that PQ = QR = PR = 5 cm.

(d). ∆DEF with m∠D = 90^{0}

(e). ∆XYZ with m∠Y= 90^{0} and XY = YZ.

(f). ∆LMN with m∠L = 30^{0}, m∠M = 70^{0} and m∠N= 80^{0}.

Answers:

(a). Triangles with lengths of sides 7 cm, 8 cm and 9 cm.

Scalene triangle.

(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

Scalene triangle.

(c). ∆PQR such that PQ = QR = PR = 5 cm.

Equilateral triangle.

(d). ∆DEF with m∠D = 90^{0}

Right-angled triangle.

(e). ∆XYZ with m∠Y= 90^{0} and XY = YZ.

Right-angled isosceles triangle.

(f). ∆LMN with m∠L = 30^{0}, m∠M = 70^{0} and m∠N= 80^{0}.

Acute angled triangle.

2). Match the following:

Measures of Triangles Types of Triangle

(i). 3 sides of equal length (a). Scalene

(ii). 2 sides of equal length (b). Isosceles right-angled

(iii). All sides are of different lengths (c). Obtuse angled

(iv). 3 acute angles (d) Right-angled

(v). 1 right angle (e). Equilateral

(vi). 1 obtuse angle (f). Acute angled

(vii). 1 right angle with two sides (g). Isosceles

of equal length.

Answers:

(i). 3 sides of equal length – Equilateral

(ii). 2 sides of equal length – Isosceles

(iii). All sides are of different lengths – Scalene

(iv). 3 acute angles – Acute angled

(v). 1 right angle – Right-angled

(vi). 1 obtuse angle – Obtuse angled

(vii). 1 right angle with two sides of equal length – Isosceles right-angled

3). Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation).

(a). acute-angled isosceles triangle.

(b). right-angled and scalene triangle.

(c). obtuse-angled isosceles triangle.

(d). right-angled isosceles triangle.

(e). acute angled and equilateral triangle.

(f). obtuse angles and scalene triangle.

4). Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with

(a). 3 matchsticks?

Yes.

(b). 4 matchsticks?

No, not possible.

(c). 5 matchsticks?

Yes.

(d). 6 matchsticks?

Yes.

(Remember you have to use all the available matchsticks in each case). Name the type of the triangle in each case. If you cannot make a triangle, think of the reason for it.)

Points to Remember

1). If all the angles in a triangle are equal, then its sides are also equal.

2). If all the sides in a triangle are equal, then its angles are also equal.

3). If two sides of a triangle are equal, it has two equal angles.

4). If none of the angles of a triangle are equal then none of the sides are equal.

5). If the three sides of a triangle are unequal then, the three angles are also unequal.

6). A triangle having all three unequal sides is called a scalene triangle.

7). A triangle having two equal sides is called an isosceles triangle.

8). A triangle having all three equal sides is called an equilateral triangle.

9). If each angle is less than 90^{0}, then the triangle is called an acute-angled triangle.

10). If anyone angle is a right angle then the triangle is called a right-angled triangle

11). If anyone angle is greater than 90^{0}, then the triangle is called an obtuse-angled triangle.

12). Equilateral triangle is also equiangular, the measure of each angle is always 60^{0}.

13). Equilateral triangle is always an acute-angle triangle.

14). Isosceles triangle can be an acute-angled, right-angled and obtuse-angled triangle.

15). Scalene triangle can be an acute-angled, right-angled and obtuse-angled triangle.

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