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

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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.

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