Page 250 - Start Up Mathematics_8 (Non CCE)

4. It is also possible to construct special types of quadrilaterals (e.g., parallelogram, rectangle, etc.)
with less than five building blocks using some other relations between these blocks.
5. If four angles and a side of a quadrilateral are given, then the quadrilateral cannot be
constructed uniquely.

Review Exercises

Multiple ChoiCe Questions
1. To construct a convex quadrilateral uniquely, it is necessary to know at least ____________ of its building
blocks.
(a) four (b) five (c) six (d) three
2. To construct a quadrilateral uniquely, we must know at least ____________ sides and two diagonals.
(a) one (b) two (c) three (d) four
3. A quadrilateral cannot be constructed uniquely, if its ____________ angles and ___________ side are
given.
(a) four, one (b) three, one (c) four, two (d) none of these
4. In a ____________ , both pairs of opposite sides are equal and all angles are of 90°.
(a) square (b) rectangle (c) rhombus (d) parallelogram
5. In a ____________ , all sides are equal and all angles are 90°.
(a) parallelogram (b) rhombus (c) square (d) rectangle

solve Mentally
True or False

1. A quadrilateral is a polygon with 4 sides, 4 enclosed angles and 2 diagonals.
2. It is possible to construct a convex quadrilateral if the measure of its 3 angles and 2 diagonals are given.
3. It is possible to construct a quadrilateral PQRS in which PQ = 3 cm, QR = 6 cm, –P = 100° and
–S = 60°.
4. Construction of a quadrilateral GLAM in which GL = 6.3 cm, –G = 100°, –L = 145°, LA = 7.8 cm and
–A = 115° is possible.
5. If in a quadrilateral EFGH, –E – –G is equal to 0 then the quadrilateral is a parallelogram.

Answer in One Word or a Line
1. Is it possible to construct a quadrilateral MPEG with MP = PE = EG = GM = 9 cm, –M = –P = –E = 95°
and –G = 75°?
2. Can you construct a rhombus if the measure of only one of its side is given? Why?
3. Name the parallelograms in which diagonals are not equal and bisect each other at right angles.
4. Can you construct a parallelogram if the measures of only two adjacent sides and the included angle is
given? How?

let’s evaluate

1. Construct a quadrilateral JUMP in which JU = 4.5 cm, UM = 7 cm, MP = JP = 6 cm and JM = 9.5 cm.
2. Construct a quadrilateral JINX in which JI = 5 cm, IN = 5 cm, JX = 4 cm, –J = 130° and –X = 50°.
3. Construct a quadrilateral DENT in which DE = 5.5 cm, EN = 4 cm, –D = 80°, –E = 100° and –N = 90°.
4. Construct a parallelogram SINK in which SI = 6.5 cm, IN = 5.5 cm and –S = 60°.
5. Construct a square BOND in which diagonal BN = 8 cm.
6. Construct a rhombus STAR in which diagonals SA = 6 cm and TR = 8 cm.

242