ople 5
c
Example 5
ce angles and their two included sides are given.
Solutions
structa quadrilateral when three angles and their
Constructa quadrilateral ABCD where AB - 4.5 cm,
BC = 52 cm, A 60, B = 100°C = 120
Steps of Construction:
(0) Draw AB4.5 cm
() Make ZABX=100
(ii) With Bas centre and radius 5.2cm drau
(v) Make BCY- 120° and BAZ = 60°
(u) LetCY and AZ intersect at D. Thus, ABCD is
52cm
0
as centre and radius 5.2 cm draw an arc which cut Bkat
intersect at D. Thus, ABCD is the required quadrilateral
1.
Exercise 12.11
Construct a quadrilateral ABCD where AB = 4cm BC 58 cm. CD = 5 cm, DA -4.8 cm and AC
7.8 cm
Construct a quadrilateral ABCD where AB - 54 cm. BC -46 cm, CD = 4.3 cm, DA = 3.5 cm ang
diagonal AC 4a
Construct a quadrilateral ABCD whene AB -4 cm, BC = 43.CD-DA = 5 cm and diagonal BD
6.1 cm
Construct a quadrilateral PQRS where PQ-3.6 cm OR 3.3 cm, PS = 2.7 cm, diagonal PR = 4
emand diagonal QS =4 cm.
m PS firm and OS = 110
Answers
Answer:
First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown. We may divide it into two conveniently constructible Δs ABC and ACD.
Steps of construction:
1. Draw AC = 7 cm.
2. With A as centre and radius 4.5 cm, draw an arc (below AC).
3. With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.
4. Join AB and BC
5. With A as centre and radius 6 cm, draw an arc (above AC).
6. With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.
7. Join AD = CD.
Then, ABCD is the required quadrilateral.
(ii) First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.
We may divide it inot two conveniently constructible Δs PJU and PMU.
Steps of construction:
1. Draw PU = 6.5 cm
2. With P as centre and radius 4.5 cm, draw an arc(below (PU)
3. With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.
4. Join PJ and JU.
5. With P as centre and radius 5 cm, draw an arc (abov PU).
6. With U as centre and radius 4 cm, draw another arc cutting the previous arc at M.
7. Join PM and UM.
Then, JUMP is the required quadrilateral.
(iii) We know that opposite sides of parallelogram are equal and parallel to each other.
∴ OR = ME and MO = ER.
Steps of Construction:
1. Draw OR = 5 cm
2. With R as centre and radius equal to 4.5 cm, cut an arc.
3. With O as centre and radius equal to 7.5 cm, cut another arc on the arc drawn in step-2 at point E.
4. With E as centre and radius equal to 6 cm, cut an arc.
5. With O as centre and radius equal to 4.5 cm, cut an arc on the arc drawn in step-4 at point M.
6. Join RE, OE, OM and ME.
Hence, MORE is the required parallelogram.
(iv) We know that all four sides of a rhombus are equal.
∴ BE = ES = ST = BT = 4.5 cm.
Steps of Construction:
1. Draw BE = 4.5 cm.
2. With B as centre and radius equal to 4.5 cm, draw an arc.
3. With E as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at point T.
4. With E as centre and radius equal to 4.5 cm, cut an arc.
5. With T as centre and radius equal to 4.5 cm, cut another arc on the previous arc at point S.
6. Join BT, ES, ET and ST.
Hence, BEST is the required rhombus.
Step-by-step explanation:
Answer:
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