Question

Construct an isosceles triangle whose altitude is 4.5 cm and vertex angle is ${70^0}.$

Answer 1

Hint- Before starting the construction first complete all the calculations ready for the making. Also make a rough diagram in order to make a clear understanding of the figure. Also for an isosceles triangle the vertex angle will be divided into equal parts by altitude.


Complete step-by-step answer:

Steps of construction:
Make a horizontal line and name it XY.
Make an arc by compass at 4.5 cm and name this point A.
Join this arc A with XY.
You will get a perpendicular line on line XY.
Vertex angle given is ${70^0}$ .
Thus the perpendicular or altitude of the triangle will divide angle A in two ${35^0}$ angles.
Use a protractor to calculate ${35^0}$ angle and mark the point there.
Join A with XY at points B and C with the help of this point on both sides of the perpendicular.
The Isosceles triangle with two equal sides is ready.
Then ABC is the required triangle.

Note- In order to solve such construction related problems. First make a horizontal base line for clear representation on the basis of that line. Making a rough diagram is very important before actual construction in order to remove the mistakes. Take extra care while drawing off the end points in order to make fewer mistakes.