Question

construct an equilateral triangle whose altitude is 4 cm give justification for your construction

Answer 1

Step-by-step explanation:

1. Draw a line XY.

2. Mark any point D on XY.

3. From D, draw DE perpendicular to XY.

4. From D, set off DA=4cm, cutting DE at A.

5. Construct angle DAC=30°, meeting XY at B and C respectively.

Then, ∆ABC is required equilateral triangle.

Verification:-

on measuring, we find that

angle A= angle B= angle C= 60°

and AB = BC = CA = 4.5 cm

Justification:-

In ∆DAB, we have

angle ABD+ angle BDA+ angle DAB =180°

=} angle ABD+ 90°+30°=180°

=} angle ABD=180°-120°= 60°

In ∆ABC, we have

angle A= angle B= angle C=60°

Hence, ∆ABC is an equilateral triangle.

Answer 2

Given : Altitude 4 cm.

To Find : Construct equilateral triangle

Solution:

Step 1 :  Draw line segment AD  = 4 cm

Step 2 :  Draw an acute angle DAX  

Step 3 : Take 3 points one by one at equal distance using suitable compass width

Step 4 : Join 3rd point with D

Step 5 : Draw a line parallel to line drawn in previous step passing through 2nd point and intersecting AD at O

Step 6 : Using Compass width = OA and taking O as center draw a circle

Step 7 : Draw a line pepepmdicular to AD at D and  intersecting circle at B and C

Step 8 : Join AB and AC

Here concept used =  Median intersection is center of circumcircle

 

Another Method :

Step 1 : Draw line segment AD = 4 cm

Step 2 : Draw a right angle at D

Step 3 : Draw an angle of 30 deg at A on AD using protractor

Step 4 : Both angles intersects at B

Step 5 : Using compass width = BD and taking D as center , intersect extended BD at C

Step 6 : Join AC

Here concept use each angle of equilateral triangle = 60 deg and  altitude bisect the angle

Learn More:

construct a right angle triangle in which base if two times of the ...

brainly.in/question/14146138

Construct triangle ABC,in which BC=5.2 cm angle ACB=45° and ...

brainly.in/question/7727032