Construct the following quadrilaterals ABCD Mention they are special quadrilaterals 43 35 cm 3.5 cm 42 3.8 CM 5.2 cm 5.10 450m AC BD 55 cm 6.5 cm 45 om 5.6 om 63 om 6.8 om 7.2 om 75 om 20 om 3.0 cm 6.7 cm 7.2 cm 83 cm 750 3.40 5.2 cm 6.3 cm 8.0 cm 5.6 cm 6.5 cm 7.4 cm 5.5 cm 6.5 cm 5.6 cm 40 cm 3.6 cm 3.8 cm 3.4 cm 3.4 cm 42 cm 5.4 cm 1050 43 cm 5.3 cm 4.8 cm 5.3 om 1200 1200 1200 neral PORS in which PR = 10 cm. PR = 2 PO. APRS is an equilateral trangle and
Answers
Answer:
Sol. Let us draw a rough sketch of the required quadrilateral and write down the given dimensions.
Steps of construction:
1. Draw EA = 5 cm
2. Make ∠XEA = 60°
3. With E as centre and radius 4 cm, cut off ED = 4 CM along EX.
4. Make ∠EAY = 90°
5. With A as centre and radius 4.5 cm, draw an arc to cut off AY at R.
6. Join DR.
Then, DEAR is the required quadrilateral.
(ii) Steps of Construction:
1. Draw RU = 3 cm.
2. Make ∠URX = 75° and ∠RUY = 120°
3. Cut off RT = 3.5 cm on RX and UE = cm on UY.
4. Join TE.
Hence, TRUE is the required quadrilateral.
EXERCISE : 4.5
Draw the following:
1. The square READ with RE = 5.1 cm.
Sol. Draw a rough sketch of the required square and write down its dimensions.
Steps of construction:
1. Draw RE = 5.1 cm
2. Draw RX ⊥ RE.
3. With R as centre and radius 5.1 cm, draw an arc to cut RX at D.
4. With D as centre and radius 5.1 cm, draw an arc.
5. With E as centre and radius 5.1 cm, draw another arc cutting the previous arc at A.
6. Join DA and EA.
Then READ is the required square.
2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
Sol. Let diagonal AC = 5.2 cm and diagonal BD = 6.4 cm
Draw AC = 5.2 cm. Draw XY, the perpendicular bisector of AC which cuts AC at O.
With O a centre, draw arcs of radii
which cut OX at D and OY at B.
Join AB, BC, CD and DA.
Then, ABCD is the required rhombus.
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
Step-by-step explanation:
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