Page 246 - Start Up Mathematics_8 (Non CCE)

Construction of Quadrilateral Given Its Three Angles and Two Included Sides

Example 9: Construct a quadrilateral MARS in which MA = 5.2 cm,
AR = 3.8 cm, –M = 100º, –A = 65º and –R = 130º.
S
Solution: Construction: Draw a rough sketch of the figure to be
constructed. R
130º
Steps of Construction: 3.8 cm
1. Draw a line MA = 5.2 cm. 100º 65º
M 5.2 cm A
M 5.2 cm A
X
Y

2. At point M on line MA, draw –AMX =
100º. Also at point A on line MA, draw
–MAY = 65º using a protractor.
3. Taking A as centre and radius = 3.8 cm, draw
an arc on line AY intersecting it at point R. 100º 65º
X M 5.2 cm A
Y
R

X

S Y
3.8 cm
R
100º 65º
M 5.2 cm A 130º 3.8 cm

4. At point R on line AR, draw –ARS = 130º
using a protractor intersecting line MX at S. 100º 65º
Join RS. M 5.2 cm A

Hence, MARS is the required quadrilateral.

Example 10: Construct a parallelogram HEAR in which HE = 5 cm, EA = 6 cm and –R = 85º. (NCERT)

Solution: Construction: Draw a rough sketch of the
figure to be constructed. H R
You know that opposite angles of a 85º
parallelogram are equal. 5 cm
5 cm
\ –E = –R = 85º
85º 95º
Also, EA ÍÍHR and AR is the transversal. E 6 cm A
\ –A + –R = 180º
( Interior angles on the same side of the transversal are supplementary.)
fi –A + 85º = 180º
fi –A = 180º – 85º = 95º
\ –A = 95º

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