From the given question, you can understand it.

Let us take some examples:

Ex1: Construct an isosceles triangle whose base is 8cm and the altitude is 4cm.

Then, draw another triangle whose sides are 1 1/2 times the corresponding sides

of the isosceles triangle.

Solution:

Construction of Triangle:

1. Draw a line segment AB = 8 cm

2. Draw two intersecting arcs at 4 cm distance from points A and B on either side of

AB.

3. Now join these arcs to get perpendicular bisector CD of AB.

4. Join A and B to C to get the triangle ABC.

Again

1. Draw a ray DX at an acute angle from point D.

2. Plot 3 points on DX so that DD₁ = D₁ D₂ = D₂ D₃

3. Now join D₂ to point B

4. Draw a line from D₃ parallel to D₂ B so that it meets the extension of AB at B₁

5. Again draw B₁ C₁ parallel to BC

6. Draw A₁ C₁ parallel to AC

So, traingle A₁ B₁ C₁ is the required traingle.

Ex2. Draw a triangle ABC with side BC=7cm, angle B =45°, angle A =105°. Then

construct a triangle whose sides are 4/3 times the corresponding sides of triangle

ABC. 

Solution:

Given ∠B = 45, ∠A = 105

Since sum of all interior angles in triangle is equal to 180

=> ∠A + ∠B + ∠C = 180

=> 105 + 45 + ∠C = 180

=> 150 + ∠C = 180

=> ∠C = 180 - 150

=> ∠C = 30

Steps of Construction:

1. Draw a triangle ABC having side BC = 7 cm, ∠B = 45, ∠C = 30

2. Now, draw a ray BX making an acute angle with BC on the opposite side of vertex A

3. Now, locate 4 points B₁ ,B₂ , B₃ ,B₄ on BX

4. Join B₃ X and draw a line through B₄ parallel to B₃ C intersecting extended BC at C₁

5. Now, through C₁ , draw a line parallel to AC intersecting extended line segment

at C₁

Now, triangle A₁ B₁ C₁ is the required triangle.

In this way, we can understand and construct the traingle either within or outside of

another triangle.