Question

construct a equilateral triangle with one of its side 6 CM

Answer 1

Answer :



Construction of an equilateral triangle of given side. (Let it be ∆ABC whose each side is 6 cm)


CONSTRUCTION -

1. Draw a line segment BC of length 6 cm.

2. At B draw angle XBC = 60°

3. Draw perpendicular bisector PQ of line segment BC.

4. Let A and D be the points where PQ intersects the ray BX and side BC respectively.

5. Join AC

Thus ABC is the required equilateral triangle.


JUSTIFICATION -

In right (rt.) ∆ABC and rt. ∆ADC,

AD = AD
【Common】

angle ADB = angle ADC
【each 90°】
【by construction】

BD = CD
【by construction】

therefore,

∆ADB ≈ ∆ADC
【by SAS rule of congruency】

therefore,

angle B = angle C = 60°
【by CPCT】

Therefore in ∆ABC third angle ;

angle A = 180° - (angle B - angle C)

= 180° - (60° + 60°)

= 180° - 120°

= 60°

Each of 3 angles of triangle is 60°. Hence constructed triangle is an equilateral.

HOPE IT WOULD HELP YOU