Similar Triangles:

If Two triangles ∆ABC and ∆PQR are said to be similar, following two conditions are

satisfied:

1. The corresponding angles of the triangles are equal.

i.e.,

∠A = ∠P, ∠B = ∠Q, ∠C = ∠R

and

2. Since ∆ABC and ∆PQR are two similar triangles, their corresponding sides are in a ratio

or proportion.

i.e.,

AB/PQ = BC/QR = AC/PR

We write ∆ABC and ∆PQR are similar as ∆ABC ~ ∆PQR

Construction of Similar Triangles:

The steps of construction of similar triangles are as follows 

1. Draw a ray BX which makes the acute angle with BC on the opposite side of vertex A.

2. Locate 5 points on the ray BX and mark them as B₁ , B₂ , B₃ , B₄ and B₅ such that

BB₁ , B₁ B₂ , B₂ B₃ , B₃B₄ and B₄ B₅ such

3. Join B₅ C

4. Draw a line parallel to B₅ C through B₃ [Since 3 is the smallest among 3 and 5] and

mark C₁ where it intersects with BC.

5. Draw a line through the point C₁ parallel to AC and mark A₁ where it intersects AB.

Hence, A₁ B C₁ is the required triangle.