Chapter 14.6, Problem 2PSA

To determine

To construct the isosceles tringle with given lengths.

Explanation of Solution

Given:

The vertex angle and the leg.

Calculation:

The isosceles triangle with given vertex angle and the leg can be constructed as follows-

Step 1- Let the vertex angel be $\angle A$ .

Step 2- Now, calculate the base angles as follows-

  $=90-\frac{\angle A}{2}$

Step 3- First draw a line and on that line draw the leg at an angle equal to the base angle.

Step 4- Draw another leg using the vertex angle and the leg to meet the base.

Step 5- Join all the points to get the required isosceles triangle ABC.

To determine

To construct the isosceles tringle with given lengths.

Explanation of Solution

Given:

The base and the altitude of the base.

Calculation:

The isosceles triangle with givenbase and the altitude of the base can be constructed as follows-

The right triangle given the hypotenuse and the altitude of the hypotenuse can be constructed as follows-

Step 1- Draw the circle as the diameter equal to the hypotenuse of the given triangle.

Step 2- Drop the perpendicular to the hypotenuse from any point on the circle whose length equals to the altitude.

Step 3- Now, join all the three points.

Step 4- Join all the vertices to get the required isosceles triangle.