6th Standard Maths Practice Set 36 Answers Chapter 15 Triangles and their Properties
The three roads together form ∆ABC.
Road AC is shorter because the sum of the lengths of any two sides (side AB + side BC) of a triangle is always greater than the third side (side AC).
Question 5
Maharashtra Board Solution
The lengths of the three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your
Solution & Step-by-Step Answer:
i. 17 cm, 7 cm, 8 cm ii. 7 cm, 24 cm, 25 cm iii. 9 cm, 6 cm, 16 cm iv. 8.4 cm, 16.4 cm, 4.9 cm v. 15 cm, 20 cm, 25 cm vi. 12 cm, 12 cm, 16 cm Solution: i. The lengths of the three sides are 17 cm, 7 cm, 8 cm. a. 7 cm + 17 cm = 24 cm, greater than 8 cm b. 8 cm +17 cm = 25 cm, greater than 7 cm c. 7 cm + 8 cm =15 cm, not greater than 17 cm The sum of lengths of two sides in (c) is not greater than the length of the third side. ∴ Triangle cannot be drawn with sides 17 cm, 7 cm, 8 cm.
ii. The lengths of the three sides are 7 cm, 24 cm, 25 cm. iii. The lengths of the three sides are 9 cm, 6 cm, 16 cm. iv. The lengths of the three sides are 8.4 cm, 16.4 cm, 4.9 cm. v. The lengths of the three sides are 15 cm, 20 cm, 25 cm. vi. The lengths of the three sides are 12 cm, 12 cm, 16 cm. Maharashtra Board Class 6 Maths Chapter 15 Triangles and their Properties Practice Set 36 Intext Questions and Activities
Question 1
Maharashtra Board Solution
In the given figure, some points and some line segments joining them have been drawn. Which of these figures is a triangle? Which figure is not a triangle? Why not? (Textbook pg. no. 77)
Solution & Step-by-Step Answer:
ABC it is a closed figure with three sides. Hence, ABC is a triangle. PQRS has three sides but it is not a closed figure. Hence, PQRS is not a triangle.
Question 2
Maharashtra Board Solution
As seen above, ∆ABC has three sides. Line segment AB is one side. Write the names of the other two sides. ∆ABC has three angles. ∠ABC is one among them. Write the names of the other angles. (Textbook pg. no. 77)
Solution & Step-by-Step Answer:
The names of other two sides are: seg BC and seg AC The names of other angles are: ∠BCA and ∠CAB
Question 3
Maharashtra Board Solution
Measure the sides of the following triangles in centimeters, using a divider and ruler. Enter the lengths in the table below. What do you observe? (Textbook pg. no. 77) |
In ∆ABC | In ∆PQR | In ∆XYZ |
l (AB) = cm | l (QR) = cm | l (XY) = cm |
l (BC) = cm | l (PQ) = cm | l (YZ) = cm |
l (AC) = cm | l (PR) = cm | l (XZ) = cm |
In ∆ABC | In ∆PQR | In ∆XYZ |
l (AB) = 2.6 cm | l (QR) = 2.8 cm | l (XY) = 2.8 cm |
l (BC) = 2.6 cm | l (PQ) = 3.8 cm | l (YZ) = 2.6 cm |
l (AC) = 2.6 cm | l (PR) = 3.8 cm | l (XZ) = 4.3 cm We observe that,
Question 4
Maharashtra Board Solution
Measure all the angles of the triangles given below. Enter them in the following table. (Textbook pg. no. 78) |
In ∆DEF | In ∆PQR | In ∆LMN |
Measure of ∠D = m ∠D =___ | Measure of ∠P = m ∠P =___ | Measure of ∠L =__ |
Measure of ∠E = m ∠E =___ | Measure of ∠Q =___=___ | Measure of ∠M =___ |
Measure of ∠F = ___=___ | Measure of ∠R =___=___ | Measure of ∠N =___ |
Observation: | Observation: | Observation: |
In ∆DEF | In ∆PQR | In ∆LMN |
Measure of ∠D = m ∠D = 60º | Measure of ∠P = m ∠P = 45º | Measure of ∠L = 30º |
Measure of ∠E = m ∠E = 68º | Measure of ∠Q = m = 90º | Measure of ∠M = 116º |
Measure of ∠F = m = 52º | Measure of ∠R = m ∠R = 45º | Measure of ∠N = 34º
Question 5
Maharashtra Board Solution
Observe the set squares in your compass box. What kind of triangles are they? (Textbook pg. no. 78)
Solution & Step-by-Step Answer:
The first set square is a scalene triangle and also a right angled triangle. The second set square is an isosceles triangle and also a right angled triangle.
Question 6
Maharashtra Board Solution
Properties of a triangle. (Textbook pg. no. 79) Take a triangular piece of paper. Choose three different colors or signs to mark the three comers of the triangle on both sides of the paper. Fold the paper at the midpoints of two sides as observe?
Solution & Step-by-Step Answer:
The three angles of the triangle form a straight angle. ∴ m∠A + m∠B + m∠C = 180° Hence, the sum of the measures of the angles of a triangle is 180°.
Question 7
Maharashtra Board Solution
Properties of a triangle (Textbook pg. no. 79) Take a triangular piece of paper and make three different types of marks near the three angles. Take a point approximately at the center of the triangle. From this point, draw three lines that meet the three sides. Cut the paper along those lines. Place the three angles side by side as shown. See how the three angles of a triangle together form a straight angle, or, an angle that measures 180°.
Solution & Step-by-Step Answer:
The three angles of the triangle form a straight angle. Hence, the sum of the measures of the angles of a triangle is 180°.
Question 8
Maharashtra Board Solution
Draw any triangle on a paper. Name its vertices A, B, C. Measure the lengths of its three sides using a divider and scale and enter them in the table. (Textbook pg. no. 79) |
Length of side | Sum of the lengths of two sides | Length of the third side |
l (AB) = cm | l (AB) + l (BC) = cm | l (AC) = cm |
l (BC) = cm | l (BC) + l (AC) = cm | l (AB) = cm |
l (AC) = cm | l (AC) + l (AB) = cm | l (BC) = cm |
Length of side | Sum of the lengths of two sides | Length of the third side |
l (AB) = 2.7 cm | l (AB) + l (BC) = 6.6 cm | l (AC) = 5.6 cm |
l (BC) = 2.9 cm | l (BC) + l (AC) = 9.5 cm | l (AB) = 2.7 cm |
l (AC) = 5.6 cm | l (AC) + l (AB) = 8.3 cm | l (BC) = 3.9 cm |