A day full of math games & activities. Find one near you.

Construct an equilateral triangle if its altitude is 6 cm. Give justification for your construction.

Solution:

Steps of Construction

1. Construct a line XY and consider a point D on this line

2. Draw perpendicular PD on the line XY

3. Now cut a line segment AD from D which is equal to 6 cm

4. Generate 30° at A on both sides of AD, i.e. ∠CAD and ∠BAD where B and C lie on the line XY

5. ABC is the required equilateral triangle

Justification

We know that

∠A = 30° + 30° = 60° and AD is perpendicular to BC

∆ABC is an equilateral triangle with AD of length 6 cm

Construct an equilateral triangle if its altitude is 6 cm. Give justification for your construction

Thus, an equilateral triangle with altitude 6 cm is constructed.

✦ Try This: Construct an equilateral triangle if its altitude is 5 cm. Give justification for your construction.

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

NCERT Exemplar Class 9 Maths Exercise 11.4 Sample Problem 1

Construct an equilateral triangle if its altitude is 6 cm. Give justification for your construction.

Summary:

An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. An equilateral triangle of altitude 6 cm is constructed above

☛ Related Questions: