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Maths 3 Mark Question

Geometrical Constructions · Maharashtra Board STD 7 (MSBSHSE - Semi English Medium). 8 questions.

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3 Mark Question

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8 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Some angles are given below. Using the symbol of congruence write the names of the pairs of congruent angles in these figures.
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Answer
i. ∠AOC ≅ ∠PQR
ii. ∠DOC ≅ ∠LMN
iii. ∠AOB ≅ ∠BOC ≅ ∠RST
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Question 23 Marks
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
Answer

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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.

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Question 33 Marks
Draw triangles with the measures given below:
In ∆PQR, l(PQ) = 6 cm, l(QR) = 3.8 cm, l(PR) = 4.5 cm.
Answer
In ∆PQR, l(PQ) = 6 cm, l(QR) = 3.8 cm, l(PR) = 4.5 cm.

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Question 43 Marks
Draw triangles with the measures given below:
In ∆STU, l(ST) = 7 cm, l(TU) = 4 cm, l(SU) = 5 cm.
Answer
In ∆STU, l(ST) = 7 cm, l(TU) = 4 cm, l(SU) = 5 cm.
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Question 53 Marks
Draw triangles with the measures given below:
In ∆ABC, l(AB) = 5.5 cm, l(BC) = 4.2 cm, l(AC) = 3.5 cm.
Answer
i. In ∆ABC, l(AB) = 5.5 cm, l(BC) = 4.2 cm, l(AC) = 3.5 cm.
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Question 63 Marks
Draw a line segment PS of length 4cm and draw its perpendicular bisector.
  1. How will your verify that CD is the perpendicular bisector? m∠CMS = __°
  2. Is l(PM) = l(SM)?
Answer

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  1. Here, m∠CMS = 90°
  2. Also, l(PM) = l(SM) = 2cm
    ∴ line CD is the perpendicular bisector of seg PS.
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Question 73 Marks
Maithili, Shaila and Ajay live in three different places in the city. A toy shop is equidistant from the three houses. Which geometrical construction should be used to represent this? Explain your answer.
Answer
Since, Maithili, Shaila and Ajay live in three different places, lines joining their houses will form a triangle.
The position of the toy shop which is equidistant from three houses can be found out by drawing the perpendicular bisector of the sides of the triangle joining the three houses.
The shop will be at the point of concurrence of the perpendicular bisectors.
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Question 83 Marks
Draw ∆ABC such that l(AB) = 4 cm, and l(BC) = 3 cm.
  1. Can this triangle be drawn ?
  2. A number of triangles can be drawn to fulfill these conditions. Try it out.
  3. Which further condition must be placed if we are to draw a unique triangle using the above information?
Answer
  1. ∆ABC triangle cannot be drawn as length of third side is not given.
  2. For ∆ABC to draw l(AC) > l(AB) + l(BC)
    i.e., l(AC) > 4 + 3
    i.e., l(AC) > 7 cm
    ∴ number of triangles can be drawn if l(AC) > 7 cm
  3. l(AC) > l(AB) + l(BC) is the required condition to draw a unique triangle.
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