- Books Name
- Rakhiedu Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 10

- Subject
- Mathmatics

**Constructions of A triangle similar to a given triangle : **

** Scale factor : **

The ratio m : n of the side of the triangle to be constructed with the corresponding sides of the given triangle is known as their scale factor.

**(I) ****Steps of construction when m < n : **

** (i)** Construct the given triangle ABC by using the given data.

** (ii)** Take any one of the three side of the given triangle as base. Let AB be the base of the given triangle.

** (iii)** At one end, say A, of the base AB below the base AB, draw a ray AX making a suitable acute angle with AB below the base AB.

** (iv)** Along AX mark n point A_{1}, A_{2}, A_{3}, ............, An such that

AA_{1} = A_{1}A_{2 }= ..............A_{n–1}An.

**Illustration 1 **

Construct a *∆*ABC in which AB = 5 cm, BC = 6 cm and AC = 7 cm. Now, construct a triangle similar to *∆*ABC such that each of its sides is two-third of the corresponding sides of *∆*ABC.

**Solution :**

** Steps of construction : **

**(i)** Draw a line segment AB = 5 cm.

** (ii) ** With A as centre and radius = 7 cm, draw an arc above AB.

** (iii)** With B as centre and radius = 6 cm, draw another arc, inter

secting the arc drawn in step (ii) at C.

** (iv)** Join AC and BC to obtain DABC.

** (v)** Below AB, draw a ray AX making a suitable acute angle with AB on opposite side of C with respect to AB.

**(vi) ** Draw three arcs (greater of 2 and 3 in 2/3) intersecting the ray AX at A_{1}, A_{2}, A_{3} such that

AA_{1} = A_{1}A_{2} = A_{2}A_{3}

**(iv)** Draw arcs (large of m and n) intersecting the ray AX at A_{1}, A_{2}, A_{3} , ..........., Am such that AA_{1} = A_{1}A_{2} = ........... = Am_{m–1} Am.

**(v) ** Join An to B.

** (vi) ** Draw a line through Am parallel to AnB, intersecting the extended line segment AB at B.

** (vii) ** Draw a line through B¢ parallel to BC intersecting the extended line segment AC at C.

** (viii) ** *∆*ABCso obtained is the required triangle.