Exercise 5.1
.) Construct the following quadrilaterals ABCD. Mention if they are special quadrilaterals.
AB
BC
CD
DA
AC
BD
ZA
ZB
2C
ZD
(i)
5.5 cm
6,8 cm
4.5 cm
5,6 cm
3.5 cm
3.5 cm
4.4 cm
3.4 cm
(iii)
6,3 cm
6.8 cm
8.0 cm
7.2 cm
4cm
7.5 cm
95°
70°
5.2 cm
8.0 cm
45°
90°
4.2 cm 5.1 cm
3.8 cm 4.5 cm
5.2 cm
3.0 cm
6.3 cm 6.7 cm
5.6 cm 7.2 cm
7.4 cm 8.3 cm
6.5 cm
4.0 cm
3.8 cm 4.3 cm
3.4 cm
5.3 cm
120°
6.5 cm
60°
105°
100°
759
(vii)
(viii)
(ix)
5.5 cm
50°
105°
80°
5.6 cm
4.8 cm
60°
3.6 cm
5.3 cm
120°
3.4 cm
(xi)
(xii)
120°
120°
60°
4.2 cm
5.4 cm
2) Construct a quadrilateral PQRS in which PR = 10 cm, PR = 2 PQ, APRS is an equilateral trangle
ZQ = 90°. (Hint: Construct APRS. With PR as diameter construct a semicircle. Find Q on this semi
Answers
Answered by
11
Explanation:
EXERCISE : 4.1
1. Construct the following quadrilaterals:
(i) Quadrilateral ABCD
(ii) Quadrilateral JUMP
AB = 4.5 cm
JU = 3.5 cm
BC = 5.5 cm
UM = 4 cm
AD = 4 cm
MP = 5 cm
AD = 6 cm
PJ = 4.5 cm
AC = 7 cm
PU = 6.5
(iii) Parallelogram MORE
(iv) Rhombus BEST
OR = 6 cm
BE = 4.5 cm
RE = 4.5 cm
ET = 6 cm
EO = 7.5 cm
Sol. (i) 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.
EXERCISE : 4.2
1. .
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
Sol. In a rectangle, opposite sides are equal and each of 4 angles is equal to 90°.
Let AB = DC = 5 and BC = 4 cm
∴AB = DC = 5 cm and BC = AD = 4 cm.
Also, ∠A = ∠B = ∠C = ∠D = 90°.
Steps of construction
1. Draw AB = 5 cm.
2. Draw ∠ABX = 90°.
3. Cut off BC = 4 cm on BX.
4. With A as centre and radius equal to 4 cm, cut off an arc.
5. With C as centre and radius equal to 5 cm cut off another arc on the arc drawn in step-4 at point D.
6. Join AD and CD.
Hence, ABCD is the required rectangle.
4. A parallelgram OKAY where OK = 5.5 cm and KA = 4.2 cm.
Sol. In order to draw a quadrilateral, we need five measurements.
But here to draw the parallelogram OKAY, we are given two consecutive sides, i.e., four sides (the opposite sides being equal). So, we need information about one of its elements more. It may be the included angle between the sides or one of the diagonals to construct a unique quadrilateral. So, the required parallelogram cannot be drawn.
hope it was helpful then please
Mark me brainlist. ☺
Similar questions