CBSE 10th Standard Maths Subject Constructions HOT Questions 2 Mark Questions With Solution 2021
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CBSE 10th Standard Maths Subject Constructions HOT Questions 2 Mark Questions With Solution 2021
10th Standard CBSE

Reg.No. :
Maths

Draw a triangle PQR, with PQ = 4 cm, angle \(\angle\) Q = 60^{o} and the median PL = 3.6 cm. Draw another triangle PQ'R' similar to given triangle \(\Delta\)PQR, such that PQ' = \(\frac { 4 }{ 3 } \) PQ.
(a) 
Draw an equilateral triangle of altitude 4 cm. Construct another triangle similar to it such that its sides are \(\frac { 2 }{ 3 } \) of the given triangle.
(a) 
Construct a triangle whose perimeter is 13.5 cm and the ratio of the three sides is 2 : 3 : 4.
(a) 
Draw a circle of diameter 8 cm. From a point P, 7 cm away from its centre, construct a pair of tangents to the circle. Measure the lengths of the tangent segments.
(a) 
Construct a tangent to a circle of radius 3 cm from a point on the concentric circle of radius 5 cm and measure its length. Also, verify the measurement by actual calculation.
(a)
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CBSE 10th Standard Maths Subject Constructions HOT Questions 2 Mark Questions With Solution 2021 Answer Keys

Steps of Construction :
1. Draw a line segment PQ = 4 cm.
2. At Q, construct an ㄥPQY = 60^{o}.
3. Through P, draw an arc of radius 3.6 cm, intersecting QY in S.
4. With S as centre and radius equal to SQ, draw an arc to intersect QY in R.
5. Join PR to get ΔPQR.
6. At P, construct an acute angle ㄥQPX ( < 90^{o}).
7. Mark four points on PX such that PP_{1 }= P_{1}P_{2 }= P_{2}P_{3 }= P_{3}P_{4}.
8. Join P_{3}Q.
9. Through P_{4}, draw P_{4}Q'  P_{3}Q, intersecting PQ in Q', when produced.
10. Through Q', draw Q'R'  QR intersecting PR in PR', when produced.
Thus, ΔPO'R' is the required triangle. 
Steps of Construction :
1. Draw any line l and take any point X on it.
2. At X, construct a right angle.
3. With X as centre and of radius 4 cm, draw an arc intersecting XY in A.
4. At A and initial line AX, draw angle of 30^{o} to each sides and let these lines intersect line I in B and C.
5. Join AB and AC to get the given triangle.
6. At B, construct an acute angle ㄥCBZ (<90^{o}).
7. Mark three points on BZ such that BB_{1}= B_{1}B_{2} = B_{2}B_{3}.
8. Join B_{3}C.
9. Through B_{2}, draw B_{2}C'  B_{3}C, intersecting line I in C'.
10. Through C', draw C'A'  CA, intersecting BA in A'. Thus, ΔA'BC' is the required triangle. 
Steps of Construction :
1. Draw a line segment AB = 13.5 cm.
2. Through A, construct an acute angle ㄥBAX ( < 90^{o}).
3. Mark nine points (2 + 3 + 4 = 9) at equal distances on AX Such that AA_{1}= A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}A_{7} = A_{7}A_{8} = A_{8}A_{9}.
4. Join A_{9}B.
5. Through A_{2} and A_{5} draw A_{5}R  A_{9}B and A_{2}Q  A_{9}B, intersecting AB in Q and R.
6. With Q as centre draw an arc of radius AQ.
7. With R as centre draw another arc of radius RB, intersecting previous arc in P.
8. Join PQ and PR
Thus, ΔPQR is the required triangle. 
5.7 cm

4 cm