3) А
can be constructed If two diagonals and
three sides are given.
Answers
Answer:
quadrilateral can be constructed uniquely if the lengths of its three sides and two diagonals are given. A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are given. A quadrilateral can be constructed uniquely if its three sides and two included angles are given.
Step-by-step explanation:
For example :
Construct a quadrilateral PQRS, where sides PS = 5 cm, SR = 3 cm & QR = 3.5 cm and diagonals PR = 5 cm & QS = 8 cm.
Solution :
1)Use ruler and draw a line segment of 5 cm. Name this line segment as PR .
2)Use compass and 5 cm wide open. With P as center, draw an arc .
3)Again use compass and 3 cm wide open. With R as center, draw an arc which cuts previous arc (made in step 2).
4)Mark point of intersection of both arcs as Point S.
5)Use ruler and join points P & S and points R & S.
6)Use ruler and measure the length of AB and DA. On measuring, you should get PS = 5 cm and SR = 3 cm (you can here notice that the measurement of PS and SR is similar to as given in the question). And we get:
7)Now, again use compass and 8 cm wide open. With S as center, draw an arc .
8)Again use compass and 3.5 cm wide open. With R as center, draw another arc which cuts previous arc (made in step 7).
9)Mark point of intersection of both arcs as Point Q .
10)Use ruler and join points P & Q, Q & S and Q & R .
11)Use ruler and measure the length of QR and QS. On measuring, you should get QR = 3.5 cm and QS = 8 cm (you can here notice that the measurement of QR and QS is similar to as given in the question). And we get resultant quadrilateral PQRS.
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