**Understanding Elementary Shapes**

**Question 1.Name the types of following triangles:**

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

**(b)**∆AJBC 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°

**(e)**∆XYZ with m∠Y = 90° and XY = YZ.

**(f)**∆LMN with m∠L = 30°, m∠M = 70° and m∠N = 80°

**Solution:****(a)** Since all the sides are of different lengths

∴ It is scalene triangle.**(b)** In ∆ABC, AB ≠ BC ≠ CA.

∴ AABC is scalene triangle.**(c)** In ∆PQR, PQ = QR = PR

∴ ∆PQR is equilateral triangle.**(d)** In ∆DEF, m∠D =90°

∴ ∆DEF is right angled triangle.**(e)** In ∆ XYZ, m∠Y = 90° and XY = YZ

∴ ∆ XYZ is an isosceles right angled.**(f)** As each angle of ∆ LMN is < 90°

∴ ∆ LMN is an acute angled triangle.

**Question 2.Match the following:**

**Solution:**

The matching is as shown:

**(i)**→ (e)

**(ii)**→ (g)

**(iii)**→ (a)

**(iv)**→ (f)

**(v)**→ (d)

**(vi)**→ (c)

**(vii)**→ (b)

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

**Solution:**

(a)Isosceles triangle; Acute angled triangle.

(a)

**(b)**Scalene triangle; Right angled triangle.

**(c)**Isosceles triangle; Obtuse angled triangle.

**(d)**Isosceles triangle; Right angled triangle.

**(e)**Equilateral triangle; Acute angled triangle.

**(f)**Scalene triangle; Obtuse angled triangle.

**Question 4.Try to construct triangles match sticks. Some are shown here. Gan you make a triangle with**

**(a)**3 matchsticks?

**(b)**4 matchsticks?

**(c)**5 matchsticks?

**(d)**6 matchsticks?

(Remember you have to use all the available matchsticks in each case)

Name the type of triangle in each case.

If you cannot make a triangle, think of reasons for it.

**Solution:**

**(a)**Yes, an equilateral triangle.

**(b)**No (as sum of two sides is always > the third side but here 1 + 1 = 2 ≱ ≯ 2).

**(c)**Yes, an isosceles triangle.

**(d)**Yes, an equilateral triangle.