Geometrical Constructions Class 7 Practice Set 6 Answers Solutions Chapter 1
Question 1
Maharashtra Board Solution
Write the names of pairs of congruent line segments. (Use a divider to find them.) i. ___ ii. ___ iii. ___ iv. ___
Solution & Step-by-Step Answer:
i. seg BG ≅ seg CG ii. seg NG ≅ seg MG ≅ seg EG ≅ seg RG
Question 2
Maharashtra Board Solution
On the line below, the distance between any two adjoining points shown on it is equal. Hence, fill in the blanks. i. seg AB ≅ seg ___ ii. seg AP ≅ seg ___ iii. seg AC ≅ seg ___ iv. seg ___ ≅ seg BY v. seg __ ≅ seg YQ vi. seg BW ≅ seg ___
Solution & Step-by-Step Answer:
i. BC ii. QW iii. QZ iv. AZ v. AY vi. AC
Note: The above problem has many solutions. Students may write solutions other than the ones given.
Maharashtra Board Class 7 Maths Chapter 1 Geometrical Constructions Practice Set 6 Intext Questions and Activities
Question 1
Maharashtra Board Solution
Try to draw triangles with the following data. Can you draw these triangles. If not, look for the reason why you could not draw so. (Textbook pg. no. 7) i. ∆ABC in which m∠A = 85°, m∠B = 115°, l(AB) = 5cm.
Solution & Step-by-Step Answer:
m∠A + m∠B = 85° + 115° = 200°>180° But the sum of the measures of the angles of a triangle is 180° Hence, ∆ABC cannot be drawn.
ii. ∆PQR in which l(QR) = 2cm, l(PQ) = 4cm, l(PR) = 2cm.
Solution:
l(QR) + l(PR) = 2 cm + 2cm
= 4 cm
= l(PQ)
But in a triangle, the sum of the length of any two sides of a triangle is always greater than the length of the third side.
Hence, ∆PQR cannot be drawn.
Question 2
Maharashtra Board Solution
Draw ∆ABC such that l(BC) = 8 cm, l(CA) = 6 cm, m∠ABC = 40°. Draw a ray to make an angle of 40° with the base BC, l(BC) = 8 cm. We have to obtain point ‘A’ on the ray. With ‘C’ as the centre, draw an arc of radius 6 cm to do so. What do we observe? The arc intersects the ray in two different points. Thus, we get two triangles of two different shapes having the given measures. (Textbook pg. no. 7)
Solution & Step-by-Step Answer:
Here ∠B is an acute angle. ∠C can be an acute angle or an obtuse angle. Hence we get two triangles of two different shapes.
Question 3
Maharashtra Board Solution
Can a triangle be drawn if the three angles are given, but not any side? How many such triangles can be drawn? (Textbook pg. no. 7)
Solution & Step-by-Step Answer:
Yes a triangle can be drawn. Since the length of side is not given, any length of side can be selected and then triangle can be constructed. We will get different triangles for different length of sides.
Question 4
Maharashtra Board Solution
Using the ruler, measure the lengths of seg AB and seg PQ. Are they of same length? Trace the seg AB on a sheet of transparent paper. Now place this new segment on PQ verify that if point A is placed on point P, then B falls on Q. (Textbook pg. no. 7) l(AB) = ___ l(PQ) = ___
Solution & Step-by-Step Answer:
l(AB) = 4 cm l(PQ) = 4 cm Since the length of two segments is the same, if placed on one another, they will coincide.
Question 5
Maharashtra Board Solution
From the shape shown below, write the names of the pairs of congruent line segments. (Textbook pg. no. 8) i. seg AB ≅ seg DC ii. seg AE ≅ seg BH iii. seg EF ≅ seg ___ iv. seg DF ≅ seg ___
Solution & Step-by-Step Answer:
seg EF ≅ seg AD ≅ seg BC ≅ seg HG seg DF ≅ seg CG ≅ seg AE ≅ seg BH
Question 6
Maharashtra Board Solution
Take a rectangular paper. Place two opposite sides upon each Other. What do you observe? (Textbook pg. no. 7)
Solution & Step-by-Step Answer:
Opposite sides of the rectangular paper coincide and hence are congruent.