# An equilateral triangle if its altitude is 3.2 cm. Construct the following and give justification

**Solution:**

We know that

In an __equilateral triangle__ all sides and angles are equal

It is given that

Altitude = 3.2 cm

Steps of Construction

1. Construct a line PQ

2. Consider a point D on PQ and construct a ray DE perpendicular to PQ

3. Now cut the line segment AD of 3.2 cm length from DE

4. Construct angles equal to 30° at the point A on both sides of AD i.e. ∠CAD and ∠BAD where B and C lie on PQ

5. Cut the line segment DC from PQ where DC = BD

6. Join AC

7. Triangle ABC is the required triangle

Justification

∠A = ∠BAD + ∠CAD

Substituting the values

∠A = 30° + 30° = 60°

AD is perpendicular to SC

∠ADS = 90°

In triangle ABD using the __angle sum property__

∠BAD + ∠DBA + ∠BDA = 180°

30° + 90° + ∠DBA = 180°

∠DBA = 60°

In the same way

∠DCA = 60°

So ∠A = ∠B = ∠C = 60°

Therefore, triangle ABC is an equilateral triangle.

**✦ Try This: **Construct each of the following and give justification: An equilateral triangle if its altitude is 4.5 cm

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 11

**NCERT Exemplar Class 9 Maths Exercise 11.4 Problem 4**

## An equilateral triangle if its altitude is 3.2 cm. Construct the following and give justification

**Summary:**

An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. An equilateral triangle of altitude 3.2 cm is constructed

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