ROAD where OA = 8 cm, AD = 7 cm, ∠ O = 105º, ∠ D = 90º, and ∠ A = 120º
Answers
Five measurements can determine a quadrilateral uniquely.
Different cases are listed and every case is explained properly. Cases of construction which are explained in this chapter are as follows:
When four sides and one diagonal are given.
When two diagonals and three sides are given.
When two adjacent sides and three angles are given.
When three sides and two included angles are given.
When other special properties are known.
Solved examples are given for reference.
After the discussion about how to do the construction of the cases listed above, some special cases are also taken.
Some examples are given to examine special cases where a quadrilateral is drawn using special properties.
Students will find questions in which they will be asked to construct rhombus, rectangle, parallelogram, etc with some specific given measurements.
Questions of this chapter can be time taking. Thus, students need to practice enough questions to improve their speed and to avoid mistakes. This chapter contains a total of 5 unsolved exercises and a summary of the chapter is also given in the end.
Page No 60:
Question 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
ANSWER:
(i) Firstly, a rough sketch of this quadrilateral can be drawn as follows.
(1) ΔABC can be constructed by using the given measurements as follows.
(2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.
(3) Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Join D to A and C.
ABCD is the required quadrilateral.
(ii)Firstly, a rough sketch of this quadrilateral can be drawn as follows.
(1) Δ JUP can be constructed by using the given measurements as follows.
(2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M.
(3) Join M to P and U.
JUMP is the required quadrilateral.
(iii)We know that opposite sides of a parallelogram are equal in length and also these are parallel to each other.
Hence, ME = OR, MO = ER
A rough sketch of this parallelogram can be drawn as follows.
(1) Δ EOR can be constructed by using the given measurements as follows.
(2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius respectively. These will intersect each other at point M.
(3) Join M to O and E.
MORE is the required parallelogram.
(iv)We know that all sides of a rhombus are of the same measure.
Hence, BE = ES = ST = TB
A rough sketch of this rhombus can be drawn as follows.
(1) Δ BET can be constructed by using the given measurements as follows.
(2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will be intersecting each other at point S.
(3) Join S to E and T.
BEST is the required rhombus.
Answer:
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