Question

1. Construct triangles with the following sides.
(i) 8 cm, 7 cm and 9 cm
(ii) 5 cm, 5.6 cm and 3.9 cm
(iii) 6.4 cm, 7.3 cm and 8.5 cm​

Answer 1

Answer:

Step-by-step explanation:

l 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

Answer 2

Construct triangles with the following sides.

(i) 8 cm, 7 cm and 9 cm

• Draw base(AB) = 8 cm
• With A as centre draw an arc with radius 7 cm
• With B as centre draw another arc with radius 9 cm which cuts the previous arc
• Name the point as C
• This triangle is called as Scalene Triangle

(ii) 5 cm, 5.6 cm and 3.9 cm

• Draw base (AB) = 5 cm
• With A as centre draw an arc with radius 5.6 cm
• With B as centre draw another arc with radius 3.9 cm which cuts the previous arc
• Name the point as C
• This triangle is called as Scalene Triangle

(iii) 6.4 cm, 7.3 cm and 8.5 cm

• Draw base (AB) = 6.4 cm
• With A as centre draw an arc with radius 7.3 cm
• With B as centre draw and other arc with radius 8.5 cm which cuts the previous arc
• Name the point as C
• This triangle is called as Scalene Triangle