**Similar figures worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on similar figures.

Two figures are similar if one can be obtained from the other by a sequence of translations, reflections, rotations, and dilations. Similar figures have the same shape but they may have different sizes.

If two figures are similar, there must be a sequence of translations, reflections, rotations, and/or dilations that can transform one to the other.

1. Identify a sequence of transformations that can transform figure A into figure B. Say whether the figures are congruent. And also, say whether they are similar.

2. Identify a sequence of transformations that can transform figure X into figure Y. Include a reflection. Say whether the figures are congruent. And also, say whether they are similar.

3. In problem 2, identify a sequence of transformations that can transform figure X into figure Y. Include a rotation.

**Problem 1 :**

Identify a sequence of transformations that can transform figure A into figure B. Say whether the figures are congruent. And also, say whether they are similar.

**Solution : **

**Step 1 : **

Both figures are squares whose orientations are the same, so no reflection or rotation is needed.

**Step 2 : **

Figure B has sides twice as long as figure A, so a dilation with a scale factor of 2 is needed.

**Step 3 :**

Figure B is moved to the right and above figure A, so a translation is needed.

**Step 4 : **

A sequence of transformations that will accomplish this is a dilation by a scale factor of 2 centered at the origin followed by the translation

(x, y) ----> (x + 4, y + 6)

The figures are not congruent, but they are similar.

**Problem 2 :**

Identify a sequence of transformations that can transform figure X into figure Y. Include a reflection. Say whether the figures are congruent. And also, say whether they are similar.

**Solution : **

**Step 1 : **

The orientation of figure Y is reversed from that of figure X, so a reflection over the y-axis is needed.

**Step 2 : **

Figure Y has sides that are half as long as figure X, so a dilation with a scale factor of 1/2 is needed.

**Step 3 :**

Figure B is moved to the right and above figure A, so a translation is needed.

**Step 4 : **

Figure Y is moved above figure X, so a translation is needed.

**Step 5 : **

A sequence of transformations that can accomplish this is a dilation by a scale factor of 1/2 centered at the origin, followed by the reflection

(x, y) ---> (-x , y)

followed by the translation

(x, y) ---> (x , y + 5)

The figures are not congruent, but they are similar.

**Problem 3 :**

In example 2, identify a sequence of transformations that can transform figure X into figure Y. Include a rotation.

**Solution : **

**Step 1 : **

The orientation of figure Y is reversed from that of figure X, so a rotation of 180º is needed.

**Step 2 : **

Figure Y has sides that are half as long as figure X, so a dilation with a scale factor of 1/2 is needed.

**Step 3 :**

Figure Y is moved above figure X, so a translation is needed.

**Step 4 : **

Figure Y is moved above figure X, so a translation is needed.

**Step 5 : **

A sequence of transformations that can accomplish, this is a rotation of 180º about the origin, followed by a dilation by a scale factor of 1/2 centered at the origin, followed by the translation

(x, y) ---> (x , y + 5)

The figures are not congruent, but they are similar.

After having gone through the stuff given above, we hope that the students would have understood "Similar figures worksheet".

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