Page No 56:
Question 1:
Construct Δ∆ PQR, in which ∠∠Q = 70∘70°, ∠∠R = 80∘80° and PQ + QR + PR = 9.5 cm.
ANSWER:

Steps of construction:
(1) Draw seg AB of 9.5 cm length.
(2) Draw a ray making angle of 35° at point A.
(3) Draw another ray making an angle of 40° at point B.
(4) Name the point of intersection of the two rays as P.
(5) Draw the perpendicular bisector of seg AP and seg BP.
Name the points as Q and R respectively where the perpendicular bisectors intersect line AB.
(6) Draw seg PQ and seg PR.
Therefore, △PQR is the required triangle.
Page No 56:
Question 2:
Construct Δ∆ XYZ, in which ∠∠Y = 58∘58°, ∠∠X = 46∘46° and perimeter of triangle is 10.5 cm.
ANSWER:

Steps of construction:
(1) Draw seg PQ of 10.5 cm length.
(2) Draw a ray making angle of 29° at point P.
(3) Draw another ray making an angle of 23° at point Q.
(4) Name the point of intersection of the two rays as Z.
(5) Draw the perpendicular bisector of seg PZ and seg QZ.
Name the points as Y and X respectively where the perpendicular bisectors intersect line PQ.
(6) Draw seg XZ and seg YZ.
Therefore, △XYZ is the required triangle.
Page No 56:
Question 3:
Construct Δ∆LMN, in which ∠∠M = 60∘60°, ∠∠N = 80∘80° and LM + MN + NL = 11 cm.
ANSWER:

Steps of construction:
(1) Draw seg AB of 11 cm length.
(2) Draw a ray making angle of 30° at point A.
(3) Draw another ray making an angle of 40° at point B.
(4) Name the point of intersection of the two rays as L.
(5) Draw the perpendicular bisector of seg AL and seg BL.
Name the points as M and N respectively where the perpendicular bisectors intersect line AB.
(6) Draw seg LM and seg LN.
Therefore, △LMN is the required triangle.
Page No 56:
Question 1:
Construct Δ∆ XYZ, such that XY + YZ =10.3 cm, YZ = 4.9 cm, ∠∠XYZ = 45∘45° .
ANSWER:

Steps of constructions:
(1) Draw seg YZ of length 4.9 cm.
(2) Draw ray YV such that ∠ZYA = 45°.
(3) Mark point W on ray YA such that YB = 10.3 cm
(4) Draw seg BZ.
(5) Construct the perpendicular bisector of seg BZ .
(6) Name the point of intersection of ray YA and the perpendicular bisector of BZ as X.
(7) Draw seg XZ.
Therefore, △XYZ is the required triangle.
Page No 56:
Question 2:
Construct Δ∆ ABC, in which ∠∠B = 70∘70°, ∠∠C = 60∘60° , AB + BC + AC = 11.2 cm.
ANSWER:

Steps of construction:
(1) Draw seg XY of 11.2 cm length.
(2) Draw a ray making angle of 35° at point X.
(3) Draw another ray making an angle of 30° at point Y.
(4) Name the point of intersection of the two rays as A.
(5) Draw the perpendicular bisector of seg AX and seg AY.
Name the points as B and C respectively where the perpendicular bisectors intersect line XY.
(6) Draw seg AB and seg AC.
Therefore, △ABC is the required triangle.
Page No 56:
Question 3:
The perimeter of a triangle is 14.4 cm and the ratio of lengths of its side is 2 : 3 : 4. Construct the triangle.
ANSWER:

Steps of construction:
1: A line AB = 14.4 cm is drawn.
2: Darw a ray AC making an acute angle at A in the downward direction. Then, divid it into (2 + 3 + 4) = 9 parts.
3: Join B and A9.
4: Draw a line parallel to BA9 at A2 and A5 intersecting AB at X and Y respectively..
5: With X as centre and XA as radius, draw an arc.
6: With Y as centre and YB as radius, draw an arc cutting the previous arc at Z.
7: Join XZ and YZ.
Hence, △XYZ is the required triangle.
Page No 56:
Question 4:
Construct Δ∆ PQR, in which PQ −- PR = 2.4 cm, QR = 6.4 cm and ∠∠PQR =
Test
Tamanna Yadav 5 years, 1 month ago
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