"Question 1 Construct the following quadrilaterals, (i) Quadrilateral DEAR DE = 4 cm EA = 5 cm AR = 4.5 cm ∠E = 60° ∠A = 90° (ii) Quadrilateral TRUE TR = 3.5 cm RU = 3 cm UE = 4 cm ∠R = 75° ∠U = 120°
Practical Geometry Page 67"
Answers
To construct a quadrilateral it is necessary to know at least 5 of its parts.
Measurement of 5 parts of a quadrilateral are sufficient to construct it in the following cases:
1. Four sides and one Diagonal.
2. Three sides and both diagonals.
3. Two adjacent sides and 3 angles.
4. Three sides and two included angles.
5. Four sides and one angle.
It is always convenient and helpful to draw a rough sketch of the quadrilateral and indicate the given measurements.
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[ Figure is in the attachment]
Steps of construction:
i)
(a) Draw a line segment DE = 4 cm.
(b) At point E, draw an angle of ∠60°
(c) Taking radius 5 cm, draw an arc from point E which intersects at A.
(d) Draw ∠A = 90° draw an arc of radius 4.5 cm with centre A which intersect at R.
(e) Join RD.
It is the required quadrilateral DEAR.
ii)
(a) Draw a line segment TR = 3.5 cm.
(b) Construct an ∠R= 75° and draw an arc of radius 3 cm with R as centre, which intersects at U.
(c) Construct an ∠U= 120° and produce the side UE.
(d) Draw an arc of radius 4 cm with U as centre.
(e) Join UE and TE.
It is the required quadrilateral TRUE.
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Hope this will help you....
