Embedded Figures, Figure Formation, Construction of Squares and Grouping of Identical Figures

**Category : **7th Class

**In this section, usually two types of problems are asked. Let us explain them briefly.**

- A simple figure (X) is provided. This figure (X) is embedded in any one of the four alternative complex figures. A student is required to identify such alternative.
- A complex figure (X) is provided. This figure embeds any one of the option simple figures. A student is required to identify such option.

**EXAMPLE**

**1. A figure (X) is given below. Choose a figure from the four options that exactly embeds the figure (X).**

(a) (b) (c) (d)

**Explanation (c):**

Figure (c) embeds the figure (X).

**Look at below:**

So, the correct option is (c).

**Figure Formation**

This section deals with the following types of problems:

**I.** **Formation of a Figure from its Segments:** In such type of problems, all the parts to form a figure are given. A student is required to identify the figure so formed out of the four options.

**II.** **Choosing a Pattern which has the same components as a given pattern:** In such type of problems, a pattern of several components is given. A pattern out of four options contains the same components. A student is required to choose such pattern.

**2. Which of the figures (a), (b), (c) and (d) can be formed from the pieces given in Fig. (X)?**

(a) (b) (c) (d)

**Explanation (d):**

Only figure (d) can be formed from the pieces given in Fig. (X).

**3. Select from the options in which the specified components of the given Fig. (X) are found. **

(a) (b) (c) (d)

**Explanation (a):**

Figure (a) consists of all the components of figure (X).

**Construction of Squares**

Such type of problems are on the basis of the geometrical figures.

A group of some geometrical figures is provided.

A student is required to identify that members of the group which can fit into each other to form a square.

**4. Select a figure from the given options which fits exactly into Fig. (X) to form a complete square.**

(a) (b) (c) (d)

**Explanation (c):**

Rotate figure (c) through 180° and then fit into Fig. (X) to obtain the following square.

So, the correct option is (c).

**Grouping of Identical Figures**

In such type of problems a set of some figures is given.

Usually these are four, six or nine in counting.

These figures are numbered as 1, 2, 3, 4.........

A candidate is required to classify these figures into groups on the basis of some common properties amongst them.

**5. Group the following figures into three classes regarding common properties amongst them.**

(a) 1, 1, 3; 4, 5, 6; 7, 8, 9

(b) 1, 3, 4; 5, 7, 8; 1, 6, 9

(c) 2, 4, 7; 5, 8, 9; 1, 3, 6

(d) 2, 5, 8; 1, 3, 4; 6, 7, 9

**Explanation (d):**

1, 5, 8 contain three different figures;

1, 3, 4 contain two similar figures;

6, 7, 9 contain a line segment.

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