Is it possible to construct a parallelogram ZEAL where ZE = 5cm, EA = 6cm and
EL = 6.5cm? Why?(Only justification is expected)
Answers
Answer:
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Answer:
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Step-by-step explanation:
1. Construct the following quadrilaterals.
(i) Quadrilateral ABCD.
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm
(ii) Quadrilateral JUMP
JU = 3.5 cm
UM = 4 cm
MP = 5 cm
PJ = 4.5 cm
PU = 6.5 cm
(iii) Parallelogram MORE
OR = 6 cm
RE = 4.5 cm
EO = 7.5 cm
(iv) Rhombus BEST
BE = 4.5 cm
ET = 6 cm
4.2.2 When two diagonals and three sides are given
When four sides and a diagonal were given, we first drew a triangle with the available data and then tried to locate the fourth point. The same technique is used here.
Example 2: Construct a quadrilateral ABCD, given that BC = 4.5 cm, AD = 5.5 cm, CD = 5 cm the diagonal AC = 5.5 cm and diagonal BD = 7 cm.
Solution:
Here is the rough sketch of the quadrilateral ABCD (Fig 4.10). Studying this sketch, we can easily see that it is possible to draw ∆ ACD first (How?).
F-4_25
Fig 4.10
Step 1 Draw ∆ ACD using SSS construction (Fig 4.11).F-4_11
Fig 4.11
(We now need to find B at a distance of 4.5 cm from C and 7 cm from D).
Step 2 With D as centre, draw an arc of radius 7 cm. (B is somewhere on this arc) (Fig 4.12).F-4_12
Fig 4.12
Step 3 With C as centre, draw an arc of radius 4.5 cm (B is somewhere on this arc also) (Fig 4.13).F-4_13
Fig 4.13
Step 4 Since B lies on both the arcs, B is the point intersection of the two arcs. Mark B and complete ABCD.F-4_26
Fig 4.14