The DAV Maths Book Class 6 Solutions and **DAV Class 6 Maths Chapter 12 Brain Teasers **Solutions of Triangles offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 12 Brain Teasers Solutions

Question 1.

A. Tick (✓) the correct answer.

(a) Which of the following can be angles of a triangle?

(i) 40°, 30°, 45°

(ii) 35°, 50°, 70°

(iii) 65°, 100°, 95°

(iv) 30°, 55°, 95°

Answer:

(iv) 30°, 55°, 95°

Sum of three angles 30°, 55° and 95° is 180°.

(b) Two equal angles of a triangle are of measure 70° each. The measure of third angle is:

(i) 20°

(ii) 50°

(iii) 40°

(iv) 60°

Answer:

(iii) 40°.

70° + 70° + x = 180°

140° + x = 180°

.-. x = 180° – 140° = 40°.

(c) The side opposite to the vertex X of ΔXYZ is ___________

(i) YZ

(ii) XY

(iii) XZ

(iv) YX

Answer:

(i) YZ.

Clearly, YZ is opposite to vertex X.

(d) A triangle can have ___________ exterior angles.

(i) 6

(ii) 4

(iii) 3

(iv) 2

Answer:

(iii) 3

Exterior angle is formed on producing one of the sides forming the triangle.

(e) Two angles of a triangle are 35° and 50° what type of triangle is this?

(i) Right angled

(ii) Obtuse angled

(iii) Acute angled

(iv) Isosceles

Answer:

(ii) Obtuse angled

The angle which is more than 90° is called obtuse angle.

B. Answer the following questions.

(a) Name the vertex opposite to side PQ of a ΔPQR.

Answer:

R

Vertex is opposite to side PQ.

(b) How many triangles are there in the given figure?

Answer:

5.

There are five triangles in the given figure.

(c) All the three sides of a triangle are equal in length. What type of triangle is this?

Answer:

Equilateral triangle.

An equilateral triangle has three equal sides.

(d) Is it possible to construct a triangle with the segments of length 5 cm, 7 cm, 12 cm? Why?

Answer:

No, sum of two line segments of a triangle should greater than the third side.

(e) Name the exterior angle formed at the vertex B of the given triangle.

Answer:

∠CBY.

Angle CBY is the exterior angle of ΔABC on producing side AB to Y.

Question 2.

A, B, C, D are 4 points. Join them in pairs. How many triangles are formed?

Answer:

Number of triangles formed by joining the given points A, B, C and D in pair is ΔABC, ΔBCD, ΔCDA, ΔADB = 4 triangles.

Question 3.

Look at the figure and fill in the blanks.

(a) 2 triangles having point X in the exterior are ___________ and ___________.

Answer:

ΔQAR and ΔPTA

(b) 2 triangles which have O as one vertex are ___________ and ___________.

Answer:

ΔAOT and ΔPOQ

(c) 2 triangles which have PT as one side are ___________ and ___________.

Answer:

ΔPTA and ΔPTQ

(d) 2 triangles having point Y in their interior are ___________ and ___________.

Answer:

ΔQSR and ΔQAR

(e) 2 triangles which have A as one vertex are ___________ and ___________

Answer:

ΔPAQ and ΔQAS

Question 3.

Fill in the blanks:

(a) The three ___________ of a triangle are non-collinear.

Answer:

vertices

(b) Side opposite to the vertex C of ΔABC is ___________

Answer:

AB

(c) Vertex opposite to the side XZ of ΔXYZ is ___________

Answer:

Y

(d) The other two angles of a right angled triangle are ___________

Answer:

acute

(e) Each angle of an equilateral triangle measures ___________

Answer:

60°

### DAV Class 6 Maths Chapter 12 HOTS

Question 1.

In the given figure, find the sum of Answer:angles ∠A, ∠B, ∠C, ∠D, ∠E, ∠F.

Answer:

In ΔABC,

∠A +∠B + ∠C = 180° …(i)

Again in ADEF,

∠D + ∠E + ∠F = 180° …(ii)

On adding (i) and (ii), we get ∠A + ∠B + ∠C + ∠D + ∠E + ∠F

= 180° + 180°

= 360°

Question 2.

Find the values of x and y.

Answer:

Here, x + 40° + 90° – 180°

x + 130° = 180°

∴ x = 180° – 130°

= 50°

Again, y + 45° + 90° = 180°

⇒ y + 135° = 180°

∴ y = 180° – 135°

= 45°.

### DAV Class 6 Maths Chapter 12 Enrichment Questions

Question 1.

Find the sum of angles of the given polygon by dividing it into triangles.

Answer:

900°

On dividing the polygon by joining its vertex it gives 5 triangles which makes a total of 5 × 180° = 900°.

Question 2.

Compute the value of x, in the following figure.

Answer:

52°.

Linear pair of

120° = 180° – 120° = 60°

Now, 60° + x° = 112°

[∵ exterior angle = sum of opposite interior angles]

⇒ x° = 112° – 60° = 52°

Additional Questions

Question 1.

Look at the figure and complete the statements:

(a) Number of all triangles are ___________.

Answer:

5

(b) Sides opposite to vertex A are ___________ and ___________.

Answer:

EF and BC

(c) Number of all the line segments is ___________.

Answer:

12

(d) Triangles with common vertex B are ___________ and ___________.

Answer:

ΔBFD and ΔBAC

(e) D is the vertex of triangle ___________, ___________ and ___________ .

Answer:

ΔDEF, ΔBDF and ΔEDC

(f) A is the vertex of triangles ___________ and ___________.

Answer:

ΔAEF and ΔABC

Question 2.

Observe the given figure and answer the following.

(a) Name all the exterior angles

(b) Interior opposite angles of ∠PRS

(c) Adjacent interior angle of ∠RQV

(d) Interior opposite angles of ∠TPR

(e) Name the exterior angle formed by QV and QS.

Answer:

(a) ∠PRS, ∠TPR and ∠VQR

(b) ∠QPR and ∠PQR

(c) ∠PQR

(d) ∠PQR and ∠PRQ

(e) ∠VQR

Question 3.

In which of the following conditions, the construction of the triangle is possible?

(a) Three angles of triangle are 40°, 60°, 80°.

(b) Three angles of triangle are 30°, 80°, 100°.

(c) The lengths of the 3 sides of a triangle are 6 cm, 3 cm, 11 cm.

(d) The three vertices of a triangle are collinear.

(e) The lengths of the three sides of a triangle are 5 cm, 12 cm and 13 cm.

(f) The three vertices of a triangle are non-collinear.

Answer:

(a) Sum of the three angles is = 40° + 60° + 80° = 180°

Hence the triangle is possible

(b) Sum of the three angles is = 30° + 80° + 100 = 210° > 180°

Hence the triangle is not possible.

(c) Sum of the two smaller sides of the triangle = 6 + 3 = 9 cm

But 9 cm <11 cm

As the sum of two sides is less than the third side.

∴ triangle is not possible.

(d) Triangle is not possible to construct as the three vertices lie on the same straight line.

(e) Sum of two smaller sides = 5 + 12 = 17 cm > 13 cm.

Hence triangle is possible.

(f) Here the three vertices are non collinear

∴ Triangle is possible.

Question 4.

Fill in the blanks:

(a) Sum of all the angles of a triangle is ___________.

Answer:

180°

(b) Sum of any two sides of a triangle is always ___________ than the third side.

Answer:

greater

(c) Three vertices of a triangle must be ___________.

Answer:

non-collinear

(d) The other two angles of a ___________ triangle are acute.

Answer:

right angled

(e) The sides of a scalene triangle are ___________ in length.

Answer:

different

(f) Each angle of an equilateral triangle is ___________.

Answer:

60°

(g) In an ___________ triangle, any two sides are equal in length.

Answer:

isosceles

(h) Exterior angle of a triangle is always ___________ than its adjacent interior angle.

Answer:

greater