Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6

Question 1.

Name the type of following triangles:

(a) Triangle 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\(\angle D \) 90°

(e) ∆XYZ with m\(\angle Y \) = 90° and XY = YZ.

(f) ∆LMN with m\(\angle L \) = 30°, m\(\angle M \) = 70° and m\(\angle N \) = 80°.

Solution:

(a) Since, 7 cm ≠ 8 cm ≠ 9 cm

i.e. all the sides are unequal The triangle is a scalene triangle.

(b) Since, AB ≠ BC ≠ AC

i.e. all the sides are unequal.

∆ABC is a scalene triangle.

(c) Since, PQ ≠ QR ≠ PR

i.e. all the sides are equal

∆PQR is an equilateral triangle.

(d) Since m\(\angle D \) = 90°

∆DEF is a right angled triangle.

(e) Since, m\(\angle Y \) = 90° and XY = YZ

i.e. two sides of the triangle are equal.

∆XYZ is an isosceles right triangle.

(f) Since m\(\angle L \) = 30°, m\(\angle M \) = 70°, m\(\angle N \) = 80°

i.e. all the angles of ∆LMN are acute.

∆LMN is an acute angled triangle.

Question 2.

Mach the following:

Solution:

Question 3.

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

Solution:

Question 4.

Try to construct triangles using matchsticks. Some are shown here. Can 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, we can make an equilateral triangle with 3 matchsticks as shown in the figure.

(b) No, we cannot make a triangle, using 4 matchsticks. [ The sum of any two sides must be greater than the third, which is not possible here.]

(c) Yes, an isosceles triangle can be made using 5 matchsticks, as shown in the figure.

(d) Yes, an equilateral triangle can be made using 6 matchsticks as shown in the figure: