**10.1 Transformations II**

**10.1.1 Similarity**

Two shapes are similar if

(a) the corresponding

**angles**are**equal**and (b) the corresponding

**sides**are**proportional**.

Example:Example:

Quadrilateral ABCD is similar to quadrilateral JKLM because

$\begin{array}{l}\angle A=\angle J={90}^{o}\\ \angle B=\angle K={50}^{o}\\ \angle C=\angle L={130}^{o}\\ \angle D=\angle M={90}^{o}\end{array}$

(All the corresponding angles are equal.)

$\begin{array}{l}\frac{AB}{JK}=\frac{5}{10}=\frac{1}{2}\\ \frac{BC}{KL}=\frac{4}{8}=\frac{1}{2}\\ \frac{CD}{LM}=\frac{2.5}{5}=\frac{1}{2}\\ \frac{AD}{JM}=\frac{3}{6}=\frac{1}{2}\end{array}$

(All the corresponding sides are proportional.)**10.1.2 Enlargement**

**1.**Enlargement is a type of transformation where all the points of an object move from a fixed point at a

**constant ratio**.

**2.**The fixed point is known as the

**centre of enlargement**and the constant ratio is known as the

**scale factor**.

$\text{Scale factor}=\frac{\text{length of side of image}}{\text{length of side of object}}$

**The object and the image are**

3.

3.

**similar**.

**4.**If

*A*’ is the image of

*A*under an enlargement with centre

*O*and scale factor

*k*, then $\frac{OA\text{'}}{OA}=k$

- if
**k > 0**, then the image is on the same side of the object. - if
**k < 0**, then the image is on the opposite side of the object. - if
**–1 <****k < 1**, then the size of the image is a reduction of the size of the object.

**5.**Area of image =

*k*

^{2}× area of object.