Maharashtra Board Class 7 Chapter 1 Set 4 Geometrical Constructions Solutions

Construct triangles of the measures given below:

Question 1. In ΔSAT, l(AT) = 6.4 cm, m∠A = 45°, m∠T = 105°.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र त्रिभुज SAT को दर्शाता है, जहाँ भुजा AT की लंबाई 6.4 सेमी है। कोण A 45° है और कोण T 105° है। एक कच्चा चित्र भी इसके निर्माण को समझने के लिए दिया गया है।
In simple words: To construct triangle SAT, draw side AT of 6.4 cm, then draw angle A at 45° and angle T at 105° using a protractor. The intersection of the rays will form point S.

🎯 Exam Tip: Always start with a rough figure to visualize the triangle and the given measurements before beginning the actual construction.

Question 2. In ΔMNP, l(NP) = 5.2 cm, m∠N = 70°, m∠P = 40°
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र त्रिभुज MNP को दर्शाता है, जहाँ भुजा NP की लंबाई 5.2 सेमी है। कोण N 70° है और कोण P 40° है। एक कच्चा चित्र भी इसके निर्माण को समझने के लिए दिया गया है।
In simple words: Construct triangle MNP by drawing side NP as 5.2 cm, then mark angle N as 70° and angle P as 40°. Point M is where the rays from N and P intersect.

🎯 Exam Tip: Ensure precise angle measurements with a protractor and accurate length measurements with a ruler for a correct construction.

Question 3. In ∆EFG, l(EG) = 6 cm, m∠F = 65°, m∠G = 45°.
Answer: In AEFG, m∠E + m∠F + m∠G = 180° ...(sum of measures of angles of a triangle) m∠E + 65° + 45° = 180° m∠E + 110° = 180° m∠E = 180°- 110° m∠E = 70°
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र त्रिभुज EFG को दर्शाता है, जहाँ भुजा EG की लंबाई 6 सेमी है। कोण F 65° है, कोण G 45° है, और कोण E 70° है। एक कच्चा चित्र भी इसके निर्माण को समझने के लिए दिया गया है।
In simple words: First, calculate the third angle, m∠E, using the angle sum property of a triangle. Then construct the triangle using the side EG and the adjacent angles E and G.

🎯 Exam Tip: When two angles and a non-included side are given, always calculate the included angle first using the angle sum property (180°) for easier construction.

Question 4. In ΔΧΥΖ, Ι(XY) = 7.3 cm, m∠X = 34°, m∠Y = 95°.
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र त्रिभुज XYZ को दर्शाता है, जहाँ भुजा XY की लंबाई 7.3 सेमी है। कोण X 34° है और कोण Y 95° है। एक कच्चा चित्र भी इसके निर्माण को समझने के लिए दिया गया है।
In simple words: To construct ΔXYZ, draw side XY with length 7.3 cm. At point X, draw an angle of 34°, and at point Y, draw an angle of 95°. The intersection of these two rays will give point Z.

🎯 Exam Tip: Accuracy in drawing the base segment and the two base angles is crucial for the correct shape and size of the triangle.

Maharashtra Board Class 7 Maths Chapter 1 Geometrical Constructions Practice Set 4 Intext Questions And Activities

Question 1. In ∆ABC, m∠A = 60°, m∠B = 40°, l(AC) = 6 cm. (Textbook pg. no. 5)
(1) Can you draw ∆ABC?
(2) What further information is required before it can be drawn?
(3) Which property can be used to get it?
(4) Draw the rough figure to find out.
Answer: (1) ∆ABC cannot be drawn using the given information. Seg AC is included inside the angles ∠A and ∠C. Since measure of ∠C is not known, the triangle cannot be drawn. (2) To draw the triangle, measure of ∠C is required. (3) The property of sum of the measures of the angles of a triangle can be used to find out m∠C. (4) In ΔΑΒC, m∠A + m∠B + m∠C = 180°
Therefore, 60° + 40° + m∠C = 180°
Therefore, 100° + m∠C = 180°
m∠C = 180°- 100°
Therefore, m∠C = 80°
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र त्रिभुज ABC का एक कच्चा रेखाचित्र है, जहाँ भुजा AC की लंबाई 6 सेमी है। कोण A 60° है, कोण B 40° है, और कोण C 80° है। यह त्रिभुज के कोणों के योग गुण को दर्शाता है।
In simple words: You cannot draw the triangle directly because the given side AC is included between angles A and C, but angle C is unknown. You need to calculate angle C first using the fact that the sum of angles in a triangle is 180°.

🎯 Exam Tip: Always check if the given side is included between the two given angles (ASA criterion) or opposite one of them. If it's not the included side, calculate the necessary angle using the angle sum property of a triangle.