Answer

Verified

429.9k+ views

**Hint:**We follow the construction as asked in the question step by step and check whether each step is correct or not. We use the fact that all the angles of an equilateral triangle have the measure ${{60}^{\circ }}$and then check whether $\angle BAC={{60}^{\circ }}$ or not. \[\]

**Complete step-by-step solution**

We are given in the question the steps of construction of an equilateral triangle one whose altitude measures 5 cm. We follow the steps one by one. \[\]

(i) We draw a line $XY$ with a rule on which one side of the equilateral triangle will lie. \[\]

(ii) We mark a point P on it which will serve as the foot of the perpendicular or altitude. This step is correct.

(iii)We draw the perpendicular line PQ of XY passing through the point P by bisecting the arc of ${{180}^{\circ }}$ with rounder at the point P. We denote Q as the point of intersection of bisecting arcs. This step is correct. \[\]

(iv) We take an arc of 5cm using the scale and the rounder and intersect PQ at a certain point. We denote the point as A. Now AP is our altitude of triangle ABC. This step is correct. \[\]

(v) We draw construct $\angle PAB={{60}^{\circ }}$and $\angle PAC={{60}^{\circ }}$ by drawing rays using the rounder and taking the arc of equal width on the point A on both side which meets $XY$ at B and C respectively.\[\]

We join AB and AC to get the triangle ABC. We know that the triangle ABC will be equilateral when all the angles are equal and of measure ${{60}^{\circ }}$ which means $\angle ABC=\angle ACB=\angle BAC={{60}^{\circ }}$, but we see that according to our construction

\[\angle BAC=\angle PAB+\angle PAC={{60}^{\circ }}+{{60}^{\circ }}={{120}^{\circ }}\]

So this step is incorrect. We are asked to find the step that does not fit in the steps of construction which we now obtained as step (v) only. So the correct choice is D.\[\]

**Note:**The obtained triangle is not equilateral but isosceles whose two angles are equal, $\angle ABC=\angle ACB={{30}^{\circ }}$. We also note that equilateral triangles must have equal sides too. If we want to make the triangle ABC equilateral we have to change the construction of construct $\angle PAB={{60}^{\circ }}$ and $\angle PAC={{60}^{\circ }}$to $\angle PAB={{30}^{\circ }}$and $\angle PAC={{30}^{\circ }}$.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What organs are located on the left side of your body class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE