Question

Construct ΔABC, such that BC = 6 cm, ∠ABC = 100° and AC - AB = 2.5cm.

Answer 1

Rough figure:

Explanation:

Here, AC – AB = 2.5 cm

∴ AC > AB

As shown in the rough figure draw seg BC = 6 cm

Draw a ray BT making an angle of 100° with BC.

Take a point D on opposite ray of BT, such that BD 2.5 cm.

Now, AD – AB = BD      ...[A-B-D]

∴ AD – AB = 2.5 cm      ...(i)

Also, AC – AB = 2.5 cm      ...(ii) [Given]

∴ AD – AB = AC – AB      ...[From (i) and (ii)]

∴ AD = AC

∴ Point A is on the perpendicular bisector of seg DC.

∴ Point A is the intersection of ray BT and the perpendicular bisector of seg DC.

​Steps of construction:

1. Draw seg BC of length 6 cm.
2. Draw ray BT, such that ∠CBT = 100°.
3. Take point D on opposite ray of BT such that l(BD) = 2.5 cm.
4. Join the points D and C.
5. Draw the perpendicular bisector of seg DC intersecting ray BT. Name the point as A.
6. Join the points A and C.

Therefore, △ABC is required triangle.