wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 4
Construct the following and give justification :
​​​​​​​
An equilateral triangle, if its altitude is 3.2cm.

Open in App
Solution

We know that in an equilateral triangle all the sides are equal and all angles are equal i.e., each angle is 60.
Given, the altitude of an equilateral triangle is 3.2cm.
Steps to construct the ΔABC.
(i) Draw a line PQ.
(ii) Take a point D on PQ and draw a ray DEPQ.
(iii) Cut the line segment AD of length 3.2cm on the ray DE.
(iv) Make angles DAB=30 at A with line AB intersecting DP.
(v) Cut the line segment DC on DQ such that DC = BD.
(vi) Join AC, thus, ΔABC is the required triangle.


Justification
Here, A=BAD+CAD
=30+30=60
Also, ADBC
ADB=90

In ΔABD, BAD+ADB+DBA=180 [angle sum property]

30+90+DBA=180 [BAD=30, by construction]

DBA=60

Similarly, DCA=60
Thus, A=B=C=60

Hence, ΔABC is an equilateral triangle.

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Construction of Triangle 3
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon